LMFDB - Embedded newform 714.2.bh.b.457.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(25,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,8,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.8
Character	$\chi$	$=$	714.457
Dual form			714.2.bh.b.25.8

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.608761 - 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.107430 + 0.816011i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(2.49739 + 0.873515i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.107430 - 0.816011i) q^{10} +(-0.516688 + 0.0680233i) q^{11} +(0.130526 - 0.991445i) q^{12} +5.83540i q^{13} +(-2.63838 - 0.197378i) q^{14} +(0.581986 + 0.581986i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.200347 + 4.11824i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.18060 - 0.584289i) q^{19} +(0.314968 + 0.760401i) q^{20} +(2.21332 - 1.44955i) q^{21} +(0.481477 - 0.199434i) q^{22} +(-2.44404 - 3.18513i) q^{23} +(0.130526 + 0.991445i) q^{24} +(4.17530 + 1.11877i) q^{25} +(-1.51031 - 5.63657i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(2.59956 - 0.492210i) q^{28} +(0.134450 - 0.0556910i) q^{29} +(-0.712784 - 0.411526i) q^{30} +(-2.92808 + 3.81595i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.260573 + 0.451326i) q^{33} +(-0.872358 - 4.02976i) q^{34} +(-0.981092 + 1.94406i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(-0.687042 - 0.0904507i) q^{37} +(-1.95507 + 1.12876i) q^{38} +(4.62954 + 3.55237i) q^{39} +(-0.501042 - 0.652971i) q^{40} +(4.13388 + 1.71231i) q^{41} +(-1.76273 + 1.97301i) q^{42} +(2.30375 - 2.30375i) q^{43} +(-0.413454 + 0.317254i) q^{44} +(0.816011 - 0.107430i) q^{45} +(3.18513 + 2.44404i) q^{46} +(-4.54751 - 2.62551i) q^{47} +(-0.382683 - 0.923880i) q^{48} +(5.47394 + 4.36302i) q^{49} -4.32259 q^{50} +(3.14525 + 2.66597i) q^{51} +(2.91770 + 5.05361i) q^{52} +(-0.772204 + 2.88190i) q^{53} +(0.991445 + 0.130526i) q^{54} -0.428931i q^{55} +(-2.38359 + 1.14825i) q^{56} +(0.863915 - 2.08568i) q^{57} +(-0.115455 + 0.0885916i) q^{58} +(8.79150 + 2.35567i) q^{59} +(0.795007 + 0.213022i) q^{60} +(11.6144 - 8.91203i) q^{61} +(1.84067 - 4.44377i) q^{62} +(0.197378 - 2.63838i) q^{63} -1.00000i q^{64} +(-4.76175 - 0.626897i) q^{65} +(0.134883 - 0.503389i) q^{66} +(0.901540 + 1.56151i) q^{67} +(1.88561 + 3.66667i) q^{68} -4.01477 q^{69} +(0.444503 - 2.13174i) q^{70} +(-0.822380 - 1.98540i) q^{71} +(0.866025 + 0.500000i) q^{72} +(1.94757 + 1.49443i) q^{73} +(0.687042 - 0.0904507i) q^{74} +(3.42934 - 2.63142i) q^{75} +(1.59631 - 1.59631i) q^{76} +(-1.34979 - 0.281454i) q^{77} +(-5.39121 - 2.23311i) q^{78} +(2.22701 + 2.90230i) q^{79} +(0.652971 + 0.501042i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-4.43620 - 0.584036i) q^{82} +(3.72085 + 3.72085i) q^{83} +(1.19202 - 2.36201i) q^{84} +(-3.33900 - 0.605906i) q^{85} +(-1.62900 + 2.82151i) q^{86} +(0.0376653 - 0.140569i) q^{87} +(0.317254 - 0.413454i) q^{88} +(2.79672 + 1.61469i) q^{89} +(-0.760401 + 0.314968i) q^{90} +(-5.09731 + 14.5733i) q^{91} +(-3.70917 - 1.53639i) q^{92} +(1.24489 + 4.64601i) q^{93} +(5.07209 + 1.35906i) q^{94} +(0.242525 + 1.84216i) q^{95} +(0.608761 + 0.793353i) q^{96} +(-13.9878 + 5.79395i) q^{97} +(-6.41666 - 2.79759i) q^{98} +(0.199434 + 0.481477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} + 8 q^{10} + 16 q^{14} + 16 q^{15} + 48 q^{16} + 8 q^{17} + 48 q^{18} - 8 q^{19} + 16 q^{22} + 24 q^{25} + 32 q^{28} - 32 q^{29} - 16 q^{33} - 48 q^{37} - 16 q^{39} + 128 q^{41} + 16 q^{42}+ \cdots + 160 q^{97}+O(q^{100}) $ 96 * q + 8 * q^5 + 8 * q^10 + 16 * q^14 + 16 * q^15 + 48 * q^16 + 8 * q^17 + 48 * q^18 - 8 * q^19 + 16 * q^22 + 24 * q^25 + 32 * q^28 - 32 * q^29 - 16 * q^33 - 48 * q^37 - 16 * q^39 + 128 * q^41 + 16 * q^42 + 48 * q^43 - 8 * q^44 - 8 * q^46 - 112 * q^49 + 64 * q^50 - 16 * q^52 - 40 * q^53 + 16 * q^57 + 16 * q^58 - 24 * q^59 + 8 * q^60 - 56 * q^70 + 24 * q^73 + 48 * q^74 - 16 * q^76 + 16 * q^77 + 32 * q^78 - 56 * q^79 - 8 * q^80 - 80 * q^83 + 80 * q^85 + 16 * q^86 - 24 * q^87 + 16 * q^90 - 40 * q^91 + 16 * q^92 - 8 * q^93 - 8 * q^94 + 80 * q^95 + 160 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.107430	+	0.816011i	−0.0480441	+	0.364931i	0.950488	+	0.310762i	$0.100584\pi$
$5$	−0.107430	+	0.816011i	−0.0480441	+	0.364931i	−0.998532	+	0.0541689i	$0.982749\pi$
$6$	−0.382683	+	0.923880i	−0.156230	+	0.377172i
$7$	2.49739	+	0.873515i	0.943926	+	0.330158i
$7$	2.49739	+	0.873515i	0.943926	+	0.330158i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	−0.107430	−	0.816011i	−0.0339723	−	0.258045i
$11$	−0.516688	+	0.0680233i	−0.155787	+	0.0205098i	−0.208016	−	0.978125i	$-0.566701\pi$
$11$	−0.516688	+	0.0680233i	−0.155787	+	0.0205098i	0.0522290	+	0.998635i	$0.483367\pi$
$12$	0.130526	−	0.991445i	0.0376797	−	0.286205i
$13$			5.83540i			1.61845i	0.587499	+	0.809225i	$0.300113\pi$
$13$			5.83540i			1.61845i	−0.587499	+	0.809225i	$0.699887\pi$
$14$	−2.63838	−	0.197378i	−0.705136	−	0.0527515i
$15$	0.581986	+	0.581986i	0.150268	+	0.150268i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.200347	+	4.11824i	−0.0485912	+	0.998819i
$17$	−0.200347	+	4.11824i	−0.0485912	+	0.998819i
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.18060	−	0.584289i	0.500263	−	0.134045i	0.000140942	−	1.00000i	$-0.499955\pi$
$19$	2.18060	−	0.584289i	0.500263	−	0.134045i	0.500122	+	0.865955i	$0.333288\pi$
$20$	0.314968	+	0.760401i	0.0704291	+	0.170031i
$21$	2.21332	−	1.44955i	0.482987	−	0.316318i
$22$	0.481477	−	0.199434i	0.102651	−	0.0425195i
$23$	−2.44404	−	3.18513i	−0.509617	−	0.664146i	0.465703	−	0.884941i	$-0.345801\pi$
$23$	−2.44404	−	3.18513i	−0.509617	−	0.664146i	−0.975320	+	0.220795i	$0.929135\pi$
$24$	0.130526	+	0.991445i	0.0266435	+	0.202378i
$25$	4.17530	+	1.11877i	0.835059	+	0.223753i
$26$	−1.51031	−	5.63657i	−0.296197	−	1.10542i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	2.59956	−	0.492210i	0.491271	−	0.0930190i
$29$	0.134450	−	0.0556910i	0.0249667	−	0.0103416i	−0.370165	−	0.928966i	$-0.620699\pi$
$29$	0.134450	−	0.0556910i	0.0249667	−	0.0103416i	0.395132	+	0.918624i	$0.370699\pi$
$30$	−0.712784	−	0.411526i	−0.130136	−	0.0751340i
$31$	−2.92808	+	3.81595i	−0.525899	+	0.685365i	−0.978476	−	0.206360i	$-0.933838\pi$
$31$	−2.92808	+	3.81595i	−0.525899	+	0.685365i	0.452577	+	0.891725i	$0.350505\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.260573	+	0.451326i	−0.0453600	+	0.0785658i
$34$	−0.872358	−	4.02976i	−0.149608	−	0.691099i
$35$	−0.981092	+	1.94406i	−0.165835	+	0.328606i
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	−0.687042	−	0.0904507i	−0.112949	−	0.0148700i	0.0738398	−	0.997270i	$-0.476475\pi$
$37$	−0.687042	−	0.0904507i	−0.112949	−	0.0148700i	−0.186789	+	0.982400i	$0.559808\pi$
$38$	−1.95507	+	1.12876i	−0.317154	+	0.183109i
$39$	4.62954	+	3.55237i	0.741319	+	0.568834i
$40$	−0.501042	−	0.652971i	−0.0792218	−	0.103244i
$41$	4.13388	+	1.71231i	0.645603	+	0.267418i	0.681366	−	0.731943i	$-0.261386\pi$
$41$	4.13388	+	1.71231i	0.645603	+	0.267418i	−0.0357631	+	0.999360i	$0.511386\pi$
$42$	−1.76273	+	1.97301i	−0.271996	+	0.304442i
$43$	2.30375	−	2.30375i	0.351319	−	0.351319i	−0.509281	−	0.860600i	$-0.670089\pi$
$43$	2.30375	−	2.30375i	0.351319	−	0.351319i	0.860600	+	0.509281i	$0.170089\pi$
$44$	−0.413454	+	0.317254i	−0.0623305	+	0.0478279i
$45$	0.816011	−	0.107430i	0.121644	−	0.0160147i
$46$	3.18513	+	2.44404i	0.469622	+	0.360354i
$47$	−4.54751	−	2.62551i	−0.663322	−	0.382969i	0.130219	−	0.991485i	$-0.458432\pi$
$47$	−4.54751	−	2.62551i	−0.663322	−	0.382969i	−0.793542	+	0.608516i	$0.791765\pi$
$48$	−0.382683	−	0.923880i	−0.0552356	−	0.133351i
$49$	5.47394	+	4.36302i	0.781992	+	0.623289i
$50$	−4.32259			−0.611306
$51$	3.14525	+	2.66597i	0.440423	+	0.373310i
$52$	2.91770	+	5.05361i	0.404612	+	0.700809i
$53$	−0.772204	+	2.88190i	−0.106070	+	0.395860i	−0.998464	−	0.0553970i	$-0.982358\pi$
$53$	−0.772204	+	2.88190i	−0.106070	+	0.395860i	0.892394	+	0.451257i	$0.149024\pi$
$54$	0.991445	+	0.130526i	0.134919	+	0.0177624i
$55$		−	0.428931i		−	0.0578371i
$56$	−2.38359	+	1.14825i	−0.318521	+	0.153442i
$57$	0.863915	−	2.08568i	0.114428	−	0.276254i
$58$	−0.115455	+	0.0885916i	−0.0151600	+	0.0116326i
$59$	8.79150	+	2.35567i	1.14456	+	0.306683i	0.780781	−	0.624805i	$-0.214821\pi$
$59$	8.79150	+	2.35567i	1.14456	+	0.306683i	0.363774	+	0.931487i	$0.381488\pi$
$60$	0.795007	+	0.213022i	0.102635	+	0.0275010i
$61$	11.6144	−	8.91203i	1.48707	−	1.14107i	0.531212	−	0.847239i	$-0.321737\pi$
$61$	11.6144	−	8.91203i	1.48707	−	1.14107i	0.955858	−	0.293830i	$-0.0949300\pi$
$62$	1.84067	−	4.44377i	0.233765	−	0.564360i
$63$	0.197378	−	2.63838i	0.0248673	−	0.332404i
$64$		−	1.00000i		−	0.125000i
$65$	−4.76175	−	0.626897i	−0.590623	−	0.0777570i
$66$	0.134883	−	0.503389i	0.0166029	−	0.0619629i
$67$	0.901540	+	1.56151i	0.110141	+	0.190769i	0.915827	−	0.401573i	$-0.131537\pi$
$67$	0.901540	+	1.56151i	0.110141	+	0.190769i	−0.805686	+	0.592343i	$0.798203\pi$
$68$	1.88561	+	3.66667i	0.228664	+	0.444649i
$69$	−4.01477			−0.483322
$70$	0.444503	−	2.13174i	0.0531283	−	0.254792i
$71$	−0.822380	−	1.98540i	−0.0975985	−	0.235624i	0.867538	−	0.497371i	$-0.165701\pi$
$71$	−0.822380	−	1.98540i	−0.0975985	−	0.235624i	−0.965136	+	0.261747i	$0.915701\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	1.94757	+	1.49443i	0.227946	+	0.174909i	0.716420	−	0.697669i	$-0.245779\pi$
$73$	1.94757	+	1.49443i	0.227946	+	0.174909i	−0.488474	+	0.872579i	$0.662446\pi$
$74$	0.687042	−	0.0904507i	0.0798670	−	0.0105147i
$75$	3.42934	−	2.63142i	0.395986	−	0.303851i
$76$	1.59631	−	1.59631i	0.183109	−	0.183109i
$77$	−1.34979	−	0.281454i	−0.153823	−	0.0320747i
$78$	−5.39121	−	2.23311i	−0.610434	−	0.252850i
$79$	2.22701	+	2.90230i	0.250559	+	0.326534i	0.901651	−	0.432464i	$-0.142356\pi$
$79$	2.22701	+	2.90230i	0.250559	+	0.326534i	−0.651093	+	0.758998i	$0.725689\pi$
$80$	0.652971	+	0.501042i	0.0730044	+	0.0560182i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−4.43620	−	0.584036i	−0.489896	−	0.0644960i
$83$	3.72085	+	3.72085i	0.408416	+	0.408416i	0.881186	−	0.472770i	$-0.156746\pi$
$83$	3.72085	+	3.72085i	0.408416	+	0.408416i	−0.472770	+	0.881186i	$0.656746\pi$
$84$	1.19202	−	2.36201i	0.130060	−	0.257717i
$85$	−3.33900	−	0.605906i	−0.362166	−	0.0657198i
$86$	−1.62900	+	2.82151i	−0.175659	+	0.304251i
$87$	0.0376653	−	0.140569i	0.00403815	−	0.0150706i
$88$	0.317254	−	0.413454i	0.0338194	−	0.0440743i
$89$	2.79672	+	1.61469i	0.296452	+	0.171157i	0.640848	−	0.767668i	$-0.278583\pi$
$89$	2.79672	+	1.61469i	0.296452	+	0.171157i	−0.344396	+	0.938825i	$0.611916\pi$
$90$	−0.760401	+	0.314968i	−0.0801533	+	0.0332006i
$91$	−5.09731	+	14.5733i	−0.534344	+	1.52770i
$92$	−3.70917	−	1.53639i	−0.386707	−	0.160179i
$93$	1.24489	+	4.64601i	0.129090	+	0.481769i
$94$	5.07209	+	1.35906i	0.523146	+	0.140176i
$95$	0.242525	+	1.84216i	0.0248825	+	0.189002i
$96$	0.608761	+	0.793353i	0.0621315	+	0.0809713i
$97$	−13.9878	+	5.79395i	−1.42025	+	0.588286i	−0.954923	−	0.296854i	$-0.904063\pi$
$97$	−13.9878	+	5.79395i	−1.42025	+	0.588286i	−0.465325	+	0.885140i	$0.654063\pi$
$98$	−6.41666	−	2.79759i	−0.648180	−	0.282600i
$99$	0.199434	+	0.481477i	0.0200439	+	0.0483903i
$100$	4.17530	−	1.11877i	0.417530	−	0.111877i
$101$	−2.26806	−	3.92839i	−0.225680	−	0.390890i	0.730843	−	0.682546i	$-0.239127\pi$
$101$	−2.26806	−	3.92839i	−0.225680	−	0.390890i	−0.956523	+	0.291656i	$0.905794\pi$
$102$	−3.72808	−	1.76108i	−0.369135	−	0.174373i
$103$	5.79872	−	10.0437i	0.571364	−	0.989632i	−0.425062	−	0.905164i	$-0.639748\pi$
$103$	5.79872	−	10.0437i	0.571364	−	0.989632i	0.996426	−	0.0844679i	$-0.0269190\pi$
$104$	−4.12625	−	4.12625i	−0.404612	−	0.404612i
$105$	0.945074	+	1.96182i	0.0922298	+	0.191454i
$106$		−	2.98357i		−	0.289790i
$107$	−1.35726	+	10.3094i	−0.131211	+	0.996646i	0.791504	+	0.611163i	$0.209298\pi$
$107$	−1.35726	+	10.3094i	−0.131211	+	0.996646i	−0.922715	+	0.385482i	$0.874035\pi$
$108$	−0.991445	+	0.130526i	−0.0954018	+	0.0125599i
$109$	−1.49489	−	11.3548i	−0.143184	−	1.08759i	−0.900597	−	0.434655i	$-0.856870\pi$
$109$	−1.49489	−	11.3548i	−0.143184	−	1.08759i	0.757413	−	0.652937i	$-0.226463\pi$
$110$	0.111016	+	0.414316i	0.0105849	+	0.0395034i
$111$	−0.490004	+	0.490004i	−0.0465091	+	0.0465091i
$112$	2.00518	−	1.72605i	0.189472	−	0.163096i
$113$	−3.38848	+	8.18051i	−0.318761	+	0.769558i	0.680559	+	0.732693i	$0.261737\pi$
$113$	−3.38848	+	8.18051i	−0.318761	+	0.769558i	−0.999320	+	0.0368647i	$0.988263\pi$
$114$	−0.294665	+	2.23821i	−0.0275979	+	0.209627i
$115$	2.86167	−	1.65218i	0.266852	−	0.154067i
$116$	0.0885916	−	0.115455i	0.00822552	−	0.0107197i
$117$	5.63657	−	1.51031i	0.521101	−	0.139629i
$118$	−9.10163			−0.837873
$119$	−4.09768	+	10.1098i	−0.375634	+	0.926768i
$120$	−0.823052			−0.0751340
$121$	−10.3628	+	2.77672i	−0.942077	+	0.252429i
$122$	−8.91203	+	11.6144i	−0.806858	+	1.05152i
$123$	3.87501	−	2.23724i	0.349398	−	0.201725i
$124$	−0.627818	+	4.76875i	−0.0563798	+	0.428247i
$125$	−2.93632	+	7.08890i	−0.262632	+	0.634051i
$126$	0.492210	+	2.59956i	0.0438496	+	0.231588i
$127$	6.12431	−	6.12431i	0.543444	−	0.543444i	−0.381093	−	0.924537i	$-0.624452\pi$
$127$	6.12431	−	6.12431i	0.543444	−	0.543444i	0.924537	+	0.381093i	$0.124452\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−0.425254	−	3.23012i	−0.0374415	−	0.284397i
$130$	4.76175	−	0.626897i	0.417633	−	0.0549825i
$131$	2.30201	−	17.4855i	0.201128	−	1.52772i	−0.531482	−	0.847070i	$-0.678365\pi$
$131$	2.30201	−	17.4855i	0.201128	−	1.52772i	0.732610	−	0.680649i	$-0.238302\pi$
$132$			0.521147i			0.0453600i
$133$	5.95619	+	0.445584i	0.516467	+	0.0386371i
$134$	−1.27497	−	1.27497i	−0.110141	−	0.110141i
$135$	0.411526	−	0.712784i	0.0354185	−	0.0613467i
$136$	−2.77037	−	3.05370i	−0.237557	−	0.261852i
$137$	−3.84637	−	6.66211i	−0.328617	−	0.569182i	0.653620	−	0.756823i	$-0.273249\pi$
$137$	−3.84637	−	6.66211i	−0.328617	−	0.569182i	−0.982238	+	0.187641i	$0.939916\pi$
$138$	3.87797	−	1.03910i	0.330115	−	0.0884540i
$139$	−3.93002	−	9.48790i	−0.333340	−	0.804753i	−0.998323	−	0.0578945i	$-0.981561\pi$
$139$	−3.93002	−	9.48790i	−0.333340	−	0.804753i	0.664983	−	0.746858i	$-0.268439\pi$
$140$	0.122378	+	2.17415i	0.0103428	+	0.183749i
$141$	−4.85130	+	2.00947i	−0.408553	+	0.169228i
$142$	1.30822	+	1.70490i	0.109783	+	0.143072i
$143$	−0.396943	−	3.01508i	−0.0331941	−	0.252134i
$144$	−0.965926	−	0.258819i	−0.0804938	−	0.0215683i
$145$	0.0310005	+	0.115696i	0.00257445	+	0.00960799i
$146$	−2.26800	−	0.939436i	−0.187701	−	0.0777483i
$147$	6.79374	−	1.68673i	0.560338	−	0.139119i
$148$	−0.640221	+	0.265188i	−0.0526258	+	0.0217983i
$149$	−19.9355	−	11.5098i	−1.63318	−	0.942917i	−0.983104	−	0.183048i	$-0.941404\pi$
$149$	−19.9355	−	11.5098i	−1.63318	−	0.942917i	−0.650076	−	0.759869i	$-0.725263\pi$
$150$	−2.63142	+	3.42934i	−0.214855	+	0.280004i
$151$	1.80054	−	6.71970i	0.146526	−	0.546841i	−0.853157	−	0.521654i	$-0.825315\pi$
$151$	1.80054	−	6.71970i	0.146526	−	0.546841i	0.999683	−	0.0251871i	$-0.00801815\pi$
$152$	−1.12876	+	1.95507i	−0.0915545	+	0.158577i
$153$	4.02976	−	0.872358i	0.325787	−	0.0705259i
$154$	1.37665	−	0.0774884i	0.110933	−	0.00624419i
$155$	−2.79930	−	2.79930i	−0.224845	−	0.224845i
$156$	5.78548	+	0.761673i	0.463209	+	0.0609826i
$157$	−3.66335	+	2.11504i	−0.292367	+	0.168798i	−0.639009	−	0.769199i	$-0.720655\pi$
$157$	−3.66335	+	2.11504i	−0.292367	+	0.168798i	0.346642	+	0.937998i	$0.387322\pi$
$158$	−2.90230	−	2.22701i	−0.230895	−	0.177172i
$159$	1.81628	+	2.36702i	0.144040	+	0.187717i
$160$	−0.760401	−	0.314968i	−0.0601150	−	0.0249004i
$161$	−3.32146	−	10.0894i	−0.261768	−	0.795159i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	2.66751	−	2.04685i	0.208935	−	0.160322i	−0.498993	−	0.866606i	$-0.666297\pi$
$163$	2.66751	−	2.04685i	0.208935	−	0.160322i	0.707928	+	0.706284i	$0.249630\pi$
$164$	4.43620	−	0.584036i	0.346409	−	0.0456056i
$165$	−0.340294	−	0.261117i	−0.0264918	−	0.0203279i
$166$	−4.55709	−	2.63104i	−0.353699	−	0.204208i
$167$	−8.21171	−	19.8248i	−0.635441	−	1.53409i	−0.832691	−	0.553737i	$-0.813201\pi$
$167$	−8.21171	−	19.8248i	−0.635441	−	1.53409i	0.197250	−	0.980353i	$-0.436799\pi$
$168$	−0.540067	+	2.59004i	−0.0416671	+	0.199826i
$169$	−21.0519			−1.61938
$170$	3.38205	−	0.278937i	0.259391	−	0.0213935i
$171$	−1.12876	−	1.95507i	−0.0863184	−	0.149508i
$172$	0.843231	−	3.14698i	0.0642958	−	0.239955i
$173$	14.5536	+	1.91602i	1.10649	+	0.145672i	0.661560	−	0.749892i	$-0.269895\pi$
$173$	14.5536	+	1.91602i	1.10649	+	0.145672i	0.444932	+	0.895564i	$0.353228\pi$
$174$			0.145528i			0.0110324i
$175$	9.45010	+	6.44119i	0.714360	+	0.486908i
$176$	−0.199434	+	0.481477i	−0.0150329	+	0.0362927i
$177$	7.22081	−	5.54072i	0.542749	−	0.416466i
$178$	−3.11934	−	0.835825i	−0.233804	−	0.0626477i
$179$	15.4364	+	4.13618i	1.15377	+	0.309153i	0.784476	−	0.620159i	$-0.212932\pi$
$179$	15.4364	+	4.13618i	1.15377	+	0.309153i	0.369297	+	0.929312i	$0.379599\pi$
$180$	0.652971	−	0.501042i	0.0486696	−	0.0373455i
$181$	−4.66144	+	11.2537i	−0.346482	+	0.836482i	0.650548	+	0.759466i	$0.274539\pi$
$181$	−4.66144	+	11.2537i	−0.346482	+	0.836482i	−0.997030	+	0.0770167i	$0.975461\pi$
$182$	1.15178	−	15.3960i	0.0853756	−	1.14123i
$183$		−	14.6396i		−	1.08219i
$184$	3.98042	+	0.524033i	0.293441	+	0.0386322i
$185$	0.147618	−	0.550916i	0.0108531	−	0.0405042i
$186$	−2.40495	−	4.16550i	−0.176340	−	0.305429i
$187$	−0.176619	−	2.14147i	−0.0129157	−	0.156600i
$188$	−5.25101			−0.382969
$189$	−1.97301	−	1.76273i	−0.143515	−	0.128220i
$190$	−0.711047	−	1.71662i	−0.0515848	−	0.124537i
$191$	−16.7556	−	9.67386i	−1.21239	−	0.699976i	−0.249114	−	0.968474i	$-0.580139\pi$
$191$	−16.7556	−	9.67386i	−1.21239	−	0.699976i	−0.963280	+	0.268498i	$0.913473\pi$
$192$	−0.793353	−	0.608761i	−0.0572553	−	0.0439336i
$193$	−4.65751	+	0.613173i	−0.335255	+	0.0441371i	−0.296274	−	0.955103i	$-0.595744\pi$
$193$	−4.65751	+	0.613173i	−0.335255	+	0.0441371i	−0.0389803	+	0.999240i	$0.512411\pi$
$194$	12.0116	−	9.21684i	0.862384	−	0.661730i
$195$	−3.39612	+	3.39612i	−0.243201	+	0.243201i
$196$	6.92208	+	1.04152i	0.494435	+	0.0743940i
$197$	−9.36208	−	3.87790i	−0.667021	−	0.276289i	0.0233688	−	0.999727i	$-0.492561\pi$
$197$	−9.36208	−	3.87790i	−0.667021	−	0.276289i	−0.690389	+	0.723438i	$0.742561\pi$
$198$	−0.317254	−	0.413454i	−0.0225463	−	0.0293829i
$199$	−11.6580	−	8.94552i	−0.826415	−	0.634131i	0.106465	−	0.994316i	$-0.466047\pi$
$199$	−11.6580	−	8.94552i	−0.826415	−	0.634131i	−0.932881	+	0.360186i	$0.882713\pi$
$200$	−3.74347	+	2.16129i	−0.264703	+	0.152826i
$201$	1.78765	+	0.235349i	0.126091	+	0.0166002i
$202$	3.20752	+	3.20752i	0.225680	+	0.225680i
$203$	0.384421	−	0.0216382i	0.0269811	−	0.00151871i
$204$	4.05685	+	0.736170i	0.284036	+	0.0515422i
$205$	−1.84136	+	3.18934i	−0.128606	+	0.222753i
$206$	−3.00164	+	11.2023i	−0.209134	+	0.780498i
$207$	−2.44404	+	3.18513i	−0.169872	+	0.221382i
$208$	5.05361	+	2.91770i	0.350405	+	0.202306i
$209$	−1.08694	+	0.450227i	−0.0751854	+	0.0311428i
$210$	−1.42063	−	1.65037i	−0.0980326	−	0.113886i
$211$	−1.98321	−	0.821472i	−0.136530	−	0.0565524i	0.313373	−	0.949630i	$-0.398541\pi$
$211$	−1.98321	−	0.821472i	−0.136530	−	0.0565524i	−0.449902	+	0.893078i	$0.648541\pi$
$212$	0.772204	+	2.88190i	0.0530352	+	0.197930i
$213$	−2.07576	−	0.556197i	−0.142229	−	0.0381100i
$214$	−1.35726	−	10.3094i	−0.0927801	−	0.704735i
$215$	1.63239	+	2.12738i	0.111328	+	0.145086i
$216$	0.923880	−	0.382683i	0.0628620	−	0.0260383i
$217$	−10.6459	+	6.97221i	−0.722689	+	0.473304i
$218$	4.38279	+	10.5810i	0.296840	+	0.716635i
$219$	2.37122	−	0.635366i	0.160232	−	0.0429340i
$220$	−0.214466	−	0.371465i	−0.0144593	−	0.0250442i
$221$	−24.0316	−	1.16910i	−1.61654	−	0.0786424i
$222$	0.346485	−	0.600130i	0.0232545	−	0.0402781i
$223$	−7.80662	−	7.80662i	−0.522770	−	0.522770i	0.395637	−	0.918407i	$-0.370524\pi$
$223$	−7.80662	−	7.80662i	−0.522770	−	0.522770i	−0.918407	+	0.395637i	$0.870524\pi$
$224$	−1.49012	+	2.18621i	−0.0995631	+	0.146073i
$225$		−	4.32259i		−	0.288172i
$226$	1.15575	−	8.77877i	0.0768792	−	0.583955i
$227$	4.02832	−	0.530338i	0.267369	−	0.0351998i	0.00435024	−	0.999991i	$-0.498615\pi$
$227$	4.02832	−	0.530338i	0.267369	−	0.0351998i	0.263019	+	0.964791i	$0.415282\pi$
$228$	−0.294665	−	2.23821i	−0.0195147	−	0.148229i
$229$	−6.18734	−	23.0915i	−0.408871	−	1.52593i	−0.796803	−	0.604239i	$-0.793477\pi$
$229$	−6.18734	−	23.0915i	−0.408871	−	1.52593i	0.387932	−	0.921688i	$-0.373190\pi$
$230$	−2.33654	+	2.33654i	−0.154067	+	0.154067i
$231$	−1.04499	+	0.899525i	−0.0687556	+	0.0591844i
$232$	−0.0556910	+	0.134450i	−0.00365629	+	0.00882707i
$233$	−1.70389	+	12.9423i	−0.111626	+	0.847881i	0.840422	+	0.541932i	$0.182307\pi$
$233$	−1.70389	+	12.9423i	−0.111626	+	0.847881i	−0.952048	+	0.305949i	$0.901026\pi$
$234$	−5.05361	+	2.91770i	−0.330365	+	0.190736i
$235$	2.63098	−	3.42876i	0.171626	−	0.223668i
$236$	8.79150	−	2.35567i	0.572278	−	0.153341i
$237$	3.65827			0.237630
$238$	1.34144	−	10.8259i	0.0869526	−	0.701740i
$239$	−2.34830			−0.151899			−0.0759495	−	0.997112i	$-0.524199\pi$
$239$	−2.34830			−0.151899			−0.0759495	+	0.997112i	$0.524199\pi$
$240$	0.795007	−	0.213022i	0.0513175	−	0.0137505i
$241$	−6.28283	+	8.18794i	−0.404712	+	0.527431i	−0.950596	−	0.310429i	$-0.899527\pi$
$241$	−6.28283	+	8.18794i	−0.404712	+	0.527431i	0.545884	+	0.837861i	$0.316194\pi$
$242$	9.29107	−	5.36420i	0.597253	−	0.344824i
$243$	−0.130526	+	0.991445i	−0.00837326	+	0.0636012i
$244$	5.60234	−	13.5252i	0.358653	−	0.865865i
$245$	−4.14834	+	3.99808i	−0.265028	+	0.255428i
$246$	−3.16393	+	3.16393i	−0.201725	+	0.201725i
$247$	3.40956	+	12.7247i	0.216945	+	0.809650i
$248$	−0.627818	−	4.76875i	−0.0398665	−	0.302816i
$249$	5.21706	−	0.686839i	0.330618	−	0.0435266i
$250$	1.00152	−	7.60733i	0.0633419	−	0.481130i
$251$			5.09722i			0.321734i	0.986976	+	0.160867i	$0.0514289\pi$
$251$			5.09722i			0.321734i	−0.986976	+	0.160867i	$0.948571\pi$
$252$	−1.14825	−	2.38359i	−0.0723333	−	0.150152i
$253$	1.47947	+	1.47947i	0.0930134	+	0.0930134i
$254$	−4.33054	+	7.50071i	−0.271722	+	0.470637i
$255$	−2.51335	+	2.28016i	−0.157392	+	0.142789i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	20.5202	−	5.49838i	1.28002	−	0.342980i	0.446157	−	0.894955i	$-0.352792\pi$
$257$	20.5202	−	5.49838i	1.28002	−	0.342980i	0.833861	+	0.551975i	$0.186126\pi$
$258$	1.24678	+	3.01000i	0.0776212	+	0.187394i
$259$	−1.63680	−	0.826032i	−0.101706	−	0.0513271i
$260$	−4.43725	+	1.83797i	−0.275186	+	0.113986i
$261$	−0.0885916	−	0.115455i	−0.00548368	−	0.00714647i
$262$	2.30201	+	17.4855i	0.142219	+	1.08026i
$263$	22.8074	+	6.11122i	1.40636	+	0.376834i	0.880626	−	0.473813i	$-0.157123\pi$
$263$	22.8074	+	6.11122i	1.40636	+	0.376834i	0.525738	+	0.850647i	$0.323789\pi$
$264$	−0.134883	−	0.503389i	−0.00830146	−	0.0309815i
$265$	−2.26871	−	0.939729i	−0.139366	−	0.0577271i
$266$	−5.86856	+	1.11117i	−0.359825	+	0.0681304i
$267$	2.98356	−	1.23583i	0.182591	−	0.0756316i
$268$	1.56151	+	0.901540i	0.0953846	+	0.0550703i
$269$	10.4575	−	13.6284i	0.637602	−	0.830939i	−0.357065	−	0.934080i	$-0.616222\pi$
$269$	10.4575	−	13.6284i	0.637602	−	0.830939i	0.994667	+	0.103141i	$0.0328891\pi$
$270$	−0.213022	+	0.795007i	−0.0129641	+	0.0483826i
$271$	−16.0884	+	27.8659i	−0.977301	+	1.69274i	−0.305178	+	0.952295i	$0.598716\pi$
$271$	−16.0884	+	27.8659i	−0.977301	+	1.69274i	−0.672123	+	0.740440i	$0.734617\pi$
$272$	3.46632	+	2.23262i	0.210177	+	0.135373i
$273$	8.45872	+	12.9156i	0.511945	+	0.781689i
$274$	5.43959	+	5.43959i	0.328617	+	0.328617i
$275$	−2.23343	−	0.294037i	−0.134681	−	0.0177311i
$276$	−3.47689	+	2.00739i	−0.209284	+	0.120830i
$277$	−16.8656	−	12.9415i	−1.01336	−	0.777576i	−0.0382406	−	0.999269i	$-0.512175\pi$
$277$	−16.8656	−	12.9415i	−1.01336	−	0.777576i	−0.975117	+	0.221692i	$0.928842\pi$
$278$	6.25175	+	8.14744i	0.374955	+	0.488651i
$279$	4.44377	+	1.84067i	0.266042	+	0.110198i
$280$	−0.680920	−	2.06839i	−0.0406927	−	0.123610i
$281$	1.35815	−	1.35815i	0.0810205	−	0.0810205i	−0.665435	−	0.746456i	$-0.731754\pi$
$281$	1.35815	−	1.35815i	0.0810205	−	0.0810205i	0.746456	+	0.665435i	$0.231754\pi$
$282$	4.16591	−	3.19661i	0.248076	−	0.190356i
$283$	18.5955	−	2.44814i	1.10539	−	0.145527i	0.444330	−	0.895863i	$-0.353442\pi$
$283$	18.5955	−	2.44814i	1.10539	−	0.145527i	0.661056	+	0.750336i	$0.270108\pi$
$284$	−1.70490	−	1.30822i	−0.101167	−	0.0776284i
$285$	1.60912	+	0.929028i	0.0953163	+	0.0550309i
$286$	1.16378	+	2.80961i	0.0688157	+	0.166136i
$287$	8.82819	+	7.88731i	0.521111	+	0.465573i
$288$	1.00000			0.0589256
$289$	−16.9197	−	1.65015i	−0.995278	−	0.0970676i
$290$	−0.0598884	−	0.103730i	−0.00351677	−	0.00609122i
$291$	−3.91860	+	14.6244i	−0.229712	+	0.857298i
$292$	2.43386	+	0.320424i	0.142431	+	0.0187514i
$293$		−	6.36234i		−	0.371692i	−0.982579	−	0.185846i	$-0.940497\pi$
$293$		−	6.36234i		−	0.371692i	0.982579	−	0.185846i	$-0.0595025\pi$
$294$	−6.12569	+	3.38761i	−0.357258	+	0.197569i
$295$	−2.86673	+	6.92089i	−0.166907	+	0.402950i
$296$	0.549770	−	0.421853i	0.0319547	−	0.0245197i
$297$	0.503389	+	0.134883i	0.0292096	+	0.00782669i
$298$	22.2352	+	5.95789i	1.28805	+	0.345132i
$299$	18.5865	−	14.2619i	1.07489	−	0.824790i
$300$	1.65418	−	3.99355i	0.0955042	−	0.230568i
$301$	7.76573	−	3.74101i	0.447609	−	0.215628i
$302$			6.95674i			0.400315i
$303$	−4.49731	−	0.592082i	−0.258364	−	0.0340142i
$304$	0.584289	−	2.18060i	0.0335113	−	0.125066i
$305$	6.02458	+	10.4349i	0.344967	+	0.597500i
$306$	−3.66667	+	1.88561i	−0.209610	+	0.107793i
$307$	20.7435			1.18390			0.591948	−	0.805976i	$-0.298359\pi$
$307$	20.7435			1.18390			0.591948	+	0.805976i	$0.298359\pi$
$308$	−1.30968	+	0.431150i	−0.0746261	+	0.0245671i
$309$	−4.43814	−	10.7146i	−0.252477	−	0.609534i
$310$	3.42842	+	1.97940i	0.194721	+	0.112422i
$311$	22.8779	+	17.5548i	1.29729	+	0.995444i	0.999163	+	0.0409175i	$0.0130281\pi$
$311$	22.8779	+	17.5548i	1.29729	+	0.995444i	0.298126	+	0.954527i	$0.403639\pi$
$312$	−5.78548	+	0.761673i	−0.327538	+	0.0431212i
$313$	−20.6174	+	15.8203i	−1.16536	+	0.894214i	−0.995823	−	0.0913091i	$-0.970895\pi$
$313$	−20.6174	+	15.8203i	−1.16536	+	0.894214i	−0.169540	+	0.985523i	$0.554228\pi$
$314$	2.99111	−	2.99111i	0.168798	−	0.168798i
$315$	2.13174	+	0.444503i	0.120110	+	0.0250449i
$316$	3.37980	+	1.39996i	0.190129	+	0.0787539i
$317$	10.8831	+	14.1832i	0.611257	+	0.796606i	0.991751	−	0.128178i	$-0.0409127\pi$
$317$	10.8831	+	14.1832i	0.611257	+	0.796606i	−0.380494	+	0.924783i	$0.624246\pi$
$318$	−2.36702	−	1.81628i	−0.132736	−	0.101852i
$319$	−0.0656805	+	0.0379206i	−0.00367740	+	0.00212315i
$320$	0.816011	+	0.107430i	0.0456164	+	0.00600551i
$321$	7.35274	+	7.35274i	0.410390	+	0.410390i
$322$	5.81962	+	8.88599i	0.324315	+	0.495197i
$323$	1.96936	+	9.09727i	0.109578	+	0.506185i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−6.52846	+	24.3645i	−0.362134	+	1.35150i
$326$	−2.04685	+	2.66751i	−0.113365	+	0.147740i
$327$	−9.91839	−	5.72639i	−0.548488	−	0.316670i
$328$	−4.13388	+	1.71231i	−0.228255	+	0.0945464i
$329$	−9.06350	−	10.5292i	−0.499687	−	0.580496i
$330$	0.396281	+	0.164145i	0.0218145	+	0.00903587i
$331$	0.778955	+	2.90710i	0.0428152	+	0.159789i	0.984024	−	0.178038i	$-0.0569750\pi$
$331$	0.778955	+	2.90710i	0.0428152	+	0.159789i	−0.941208	+	0.337826i	$0.890308\pi$
$332$	5.08277	+	1.36193i	0.278953	+	0.0747454i
$333$	0.0904507	+	0.687042i	0.00495667	+	0.0376496i
$334$	13.0629	+	17.0240i	0.714772	+	0.931510i
$335$	−1.37106	+	0.567913i	−0.0749092	+	0.0310284i
$336$	−0.148688	−	2.64157i	−0.00811160	−	0.144109i
$337$	−6.91104	−	16.6847i	−0.376468	−	0.908875i	−0.992622	−	0.121249i	$-0.961310\pi$
$337$	−6.91104	−	16.6847i	−0.376468	−	0.908875i	0.616154	−	0.787626i	$-0.288690\pi$
$338$	20.3346	−	5.44864i	1.10606	−	0.296367i
$339$	4.42726	+	7.66824i	0.240456	+	0.416482i
$340$	−3.19461	+	1.14477i	−0.173252	+	0.0620839i
$341$	1.25333	−	2.17084i	0.0678718	−	0.117557i
$342$	1.59631	+	1.59631i	0.0863184	+	0.0863184i
$343$	9.85942	+	15.6777i	0.532359	+	0.846519i
$344$			3.25800i			0.175659i
$345$	0.431306	−	3.27610i	0.0232208	−	0.176379i
$346$	−14.5536	+	1.91602i	−0.782408	+	0.103006i
$347$	−1.13060	−	8.58772i	−0.0606935	−	0.461013i	−0.994624	−	0.103557i	$-0.966978\pi$
$347$	−1.13060	−	8.58772i	−0.0606935	−	0.461013i	0.933930	−	0.357456i	$-0.116356\pi$
$348$	−0.0376653	−	0.140569i	−0.00201907	−	0.00753528i
$349$	−7.48198	+	7.48198i	−0.400501	+	0.400501i	−0.878410	−	0.477909i	$-0.841395\pi$
$349$	−7.48198	+	7.48198i	−0.400501	+	0.400501i	0.477909	+	0.878410i	$0.341395\pi$
$350$	−10.7952	−	3.77584i	−0.577027	−	0.201827i
$351$	2.23311	−	5.39121i	0.119195	−	0.287761i
$352$	0.0680233	−	0.516688i	0.00362565	−	0.0275396i
$353$	16.3512	−	9.44039i	0.870288	−	0.502461i	0.00284423	−	0.999996i	$-0.499095\pi$
$353$	16.3512	−	9.44039i	0.870288	−	0.502461i	0.867444	+	0.497535i	$0.165761\pi$
$354$	−5.54072	+	7.22081i	−0.294486	+	0.383782i
$355$	1.70846	−	0.457780i	0.0906755	−	0.0242964i
$356$	3.22938			0.171157
$357$	5.52617	+	9.40540i	0.292476	+	0.497786i
$358$	−15.9810			−0.844620
$359$	−18.2805	+	4.89825i	−0.964809	+	0.258520i	−0.706635	−	0.707579i	$-0.749788\pi$
$359$	−18.2805	+	4.89825i	−0.964809	+	0.258520i	−0.258174	+	0.966098i	$0.583121\pi$
$360$	−0.501042	+	0.652971i	−0.0264073	+	0.0344146i
$361$	−12.0409	+	6.95180i	−0.633730	+	0.365884i
$362$	1.58993	−	12.0767i	0.0835649	−	0.634739i
$363$	−4.10558	+	9.91175i	−0.215487	+	0.520232i
$364$	2.87224	+	15.1695i	0.150547	+	0.795098i
$365$	−1.42870	+	1.42870i	−0.0747814	+	0.0747814i
$366$	3.78901	+	14.1408i	0.198055	+	0.739150i
$367$	−1.24287	−	9.44052i	−0.0648772	−	0.492791i	−0.992778	−	0.119965i	$-0.961722\pi$
$367$	−1.24287	−	9.44052i	−0.0648772	−	0.492791i	0.927901	−	0.372827i	$-0.121611\pi$
$368$	−3.98042	+	0.524033i	−0.207494	+	0.0273171i
$369$	0.584036	−	4.43620i	0.0304037	−	0.230939i
$370$			0.570350i			0.0296511i
$371$	−4.44588	+	6.52272i	−0.230819	+	0.338643i
$372$	3.40112	+	3.40112i	0.176340	+	0.176340i
$373$	−16.4708	+	28.5283i	−0.852825	+	1.47714i	0.0258223	+	0.999667i	$0.491780\pi$
$373$	−16.4708	+	28.5283i	−0.852825	+	1.47714i	−0.878648	+	0.477470i	$0.841554\pi$
$374$	0.724855	+	2.02279i	0.0374814	+	0.104596i
$375$	3.83649	+	6.64499i	0.198115	+	0.343146i
$376$	5.07209	−	1.35906i	0.261573	−	0.0700882i
$377$	0.324979	+	0.784570i	0.0167373	+	0.0404074i
$378$	2.36201	+	1.19202i	0.121489	+	0.0613108i
$379$	24.0340	−	9.95520i	1.23454	−	0.511364i	0.332537	−	0.943090i	$-0.392095\pi$
$379$	24.0340	−	9.95520i	1.23454	−	0.511364i	0.902005	+	0.431726i	$0.142095\pi$
$380$	1.13111	+	1.47409i	0.0580249	+	0.0756195i
$381$	−1.13050	−	8.58698i	−0.0579171	−	0.439924i
$382$	18.6885	+	5.00756i	0.956185	+	0.256209i
$383$	8.37234	+	31.2460i	0.427806	+	1.59660i	0.757717	+	0.652583i	$0.226315\pi$
$383$	8.37234	+	31.2460i	0.427806	+	1.59660i	−0.329911	+	0.944012i	$0.607019\pi$
$384$	0.923880	+	0.382683i	0.0471465	+	0.0195287i
$385$	0.374678	−	1.07121i	0.0190953	−	0.0545939i
$386$	4.34011	−	1.79773i	0.220906	−	0.0915021i
$387$	−2.82151	−	1.62900i	−0.143425	−	0.0828066i
$388$	−9.21684	+	12.0116i	−0.467914	+	0.609797i
$389$	7.89219	−	29.4540i	0.400150	−	1.49338i	−0.412679	−	0.910877i	$-0.635407\pi$
$389$	7.89219	−	29.4540i	0.400150	−	1.49338i	0.812829	−	0.582503i	$-0.197926\pi$
$390$	2.40142	−	4.15938i	0.121601	−	0.210619i
$391$	13.6068	−	9.42699i	0.688124	−	0.476744i
$392$	−6.95578	+	0.785540i	−0.351320	+	0.0396758i
$393$	−12.4708	−	12.4708i	−0.629070	−	0.629070i
$394$	10.0468	+	1.32268i	0.506148	+	0.0666356i
$395$	−2.60756	+	1.50547i	−0.131200	+	0.0757486i
$396$	0.413454	+	0.317254i	0.0207768	+	0.0159426i
$397$	−10.7043	−	13.9501i	−0.537234	−	0.700137i	0.443325	−	0.896361i	$-0.353799\pi$
$397$	−10.7043	−	13.9501i	−0.537234	−	0.700137i	−0.980559	+	0.196224i	$0.937132\pi$
$398$	13.5761	+	5.62339i	0.680506	+	0.281875i
$399$	3.97940	−	4.45411i	0.199219	−	0.222984i
$400$	3.05653	−	3.05653i	0.152826	−	0.152826i
$401$	22.7070	−	17.4237i	1.13393	−	0.870098i	0.141146	−	0.989989i	$-0.454921\pi$
$401$	22.7070	−	17.4237i	1.13393	−	0.870098i	0.992787	+	0.119891i	$0.0382545\pi$
$402$	−1.78765	+	0.235349i	−0.0891601	+	0.0117381i
$403$	−22.2676	−	17.0865i	−1.10923	−	0.851142i
$404$	−3.92839	−	2.26806i	−0.195445	−	0.112840i
$405$	−0.314968	−	0.760401i	−0.0156509	−	0.0377846i
$406$	−0.365722	+	0.120396i	−0.0181505	+	0.00597518i
$407$	0.361139			0.0179010
$408$	−4.10915	+	0.338905i	−0.203433	+	0.0167783i
$409$	11.0793	+	19.1899i	0.547836	+	0.948880i	0.998423	+	0.0561469i	$0.0178815\pi$
$409$	11.0793	+	19.1899i	0.547836	+	0.948880i	−0.450587	+	0.892733i	$0.648785\pi$
$410$	0.953160	−	3.55724i	0.0470732	−	0.175680i
$411$	−7.62692	−	1.00410i	−0.376208	−	0.0495288i
$412$		−	11.5974i		−	0.571364i
$413$	19.8981	+	13.5625i	0.979122	+	0.667369i
$414$	1.53639	−	3.70917i	0.0755093	−	0.182296i
$415$	−3.43598	+	2.63652i	−0.168666	+	0.129422i
$416$	−5.63657	−	1.51031i	−0.276355	−	0.0740492i
$417$	−9.91970	−	2.65797i	−0.485770	−	0.130162i
$418$	0.933379	−	0.716207i	0.0456531	−	0.0350308i
$419$	6.47099	−	15.6224i	0.316129	−	0.763202i	−0.683324	−	0.730115i	$-0.739466\pi$
$419$	6.47099	−	15.6224i	0.316129	−	0.763202i	0.999452	−	0.0330867i	$-0.0105337\pi$
$420$	1.79937	+	1.22645i	0.0878002	+	0.0598446i
$421$		−	25.3125i		−	1.23366i	−0.787097	−	0.616829i	$-0.788417\pi$
$421$		−	25.3125i		−	1.23366i	0.787097	−	0.616829i	$-0.211583\pi$
$422$	2.12824	+	0.280189i	0.103601	+	0.0136394i
$423$	−1.35906	+	5.07209i	−0.0660798	+	0.246613i
$424$	−1.49178	−	2.58384i	−0.0724474	−	0.125483i
$425$	−5.44385	+	16.9707i	−0.264066	+	0.823200i
$426$	2.14898			0.104119
$427$	36.7905	−	12.1115i	1.78042	−	0.586117i
$428$	3.97927	+	9.60681i	0.192345	+	0.464363i
$429$	−2.63367	−	1.52055i	−0.127155	−	0.0734129i
$430$	−2.12738	−	1.63239i	−0.102591	−	0.0787210i
$431$	−23.9917	+	3.15857i	−1.15564	+	0.152143i	−0.683888	−	0.729587i	$-0.739712\pi$
$431$	−23.9917	+	3.15857i	−1.15564	+	0.152143i	−0.471754	+	0.881730i	$0.656379\pi$
$432$	−0.793353	+	0.608761i	−0.0381702	+	0.0292890i
$433$	−1.52328	+	1.52328i	−0.0732041	+	0.0732041i	−0.742761	−	0.669557i	$-0.766484\pi$
$433$	−1.52328	+	1.52328i	−0.0732041	+	0.0732041i	0.669557	+	0.742761i	$0.266484\pi$
$434$	8.47858	−	9.48999i	0.406985	−	0.455534i
$435$	0.110659	+	0.0458366i	0.00530571	+	0.00219770i
$436$	−6.97201	−	9.08610i	−0.333899	−	0.435145i
$437$	−7.19050	−	5.51746i	−0.343968	−	0.263936i
$438$	−2.12597	+	1.22743i	−0.101583	+	0.0586490i
$439$	−12.4373	−	1.63740i	−0.593600	−	0.0781489i	−0.172260	−	0.985052i	$-0.555107\pi$
$439$	−12.4373	−	1.63740i	−0.593600	−	0.0781489i	−0.421340	+	0.906903i	$0.638440\pi$
$440$	0.303300	+	0.303300i	0.0144593	+	0.0144593i
$441$	2.79759	−	6.41666i	0.133219	−	0.305555i
$442$	23.5153	−	5.09056i	1.11851	−	0.242133i
$443$	−3.81756	+	6.61221i	−0.181378	+	0.314156i	−0.942350	−	0.334629i	$-0.891389\pi$
$443$	−3.81756	+	6.61221i	−0.181378	+	0.314156i	0.760972	+	0.648785i	$0.224722\pi$
$444$	−0.179354	+	0.669358i	−0.00851176	+	0.0317663i
$445$	−1.61806	+	2.10869i	−0.0767032	+	0.0999616i
$446$	9.56112	+	5.52012i	0.452732	+	0.261385i
$447$	−21.2673	+	8.80920i	−1.00591	+	0.416661i
$448$	0.873515	−	2.49739i	0.0412697	−	0.117991i
$449$	−7.63521	−	3.16261i	−0.360328	−	0.149253i	0.195173	−	0.980769i	$-0.437473\pi$
$449$	−7.63521	−	3.16261i	−0.360328	−	0.149253i	−0.555501	+	0.831516i	$0.687473\pi$
$450$	1.11877	+	4.17530i	0.0527392	+	0.196825i
$451$	−2.25240	−	0.603530i	−0.106062	−	0.0284191i
$452$	1.15575	+	8.77877i	0.0543618	+	0.412919i
$453$	−4.23500	−	5.51915i	−0.198977	−	0.259312i
$454$	−3.75379	+	1.55487i	−0.176174	+	0.0729738i
$455$	−11.3444	−	5.72507i	−0.531832	−	0.268395i
$456$	0.863915	+	2.08568i	0.0404565	+	0.0976707i
$457$	29.5100	−	7.90717i	1.38042	−	0.369882i	0.509145	−	0.860681i	$-0.329962\pi$
$457$	29.5100	−	7.90717i	1.38042	−	0.369882i	0.871273	+	0.490799i	$0.163295\pi$
$458$	11.9530	+	20.7032i	0.558528	+	0.967399i
$459$	1.76108	−	3.72808i	0.0822000	−	0.174012i
$460$	1.65218	−	2.86167i	0.0770335	−	0.133426i
$461$	2.53233	+	2.53233i	0.117942	+	0.117942i	0.763615	−	0.645672i	$-0.223423\pi$
$461$	2.53233	+	2.53233i	0.117942	+	0.117942i	−0.645672	+	0.763615i	$0.723423\pi$
$462$	0.776573	−	1.13934i	0.0361295	−	0.0530068i
$463$			21.0221i			0.976979i	0.872570	+	0.488489i	$0.162452\pi$
$463$			21.0221i			0.976979i	−0.872570	+	0.488489i	$0.837548\pi$
$464$	0.0189952	−	0.144283i	0.000881828	−	0.00669815i
$465$	−3.92493	+	0.516727i	−0.182014	+	0.0239627i
$466$	−1.70389	−	12.9423i	−0.0789313	−	0.599543i
$467$	6.89849	+	25.7455i	0.319224	+	1.19136i	0.919992	+	0.391937i	$0.128195\pi$
$467$	6.89849	+	25.7455i	0.319224	+	1.19136i	−0.600768	+	0.799423i	$0.705139\pi$
$468$	4.12625	−	4.12625i	0.190736	−	0.190736i
$469$	0.887494	+	4.68722i	0.0409807	+	0.216436i
$470$	−1.65390	+	3.99287i	−0.0762888	+	0.184178i
$471$	−0.552136	+	4.19389i	−0.0254411	+	0.193244i
$472$	−7.88224	+	4.55081i	−0.362809	+	0.209468i
$473$	−1.03361	+	1.34703i	−0.0475256	+	0.0619365i
$474$	−3.53362	+	0.946830i	−0.162304	+	0.0434893i
$475$	9.75832			0.447742
$476$	1.50622	+	10.8042i	0.0690377	+	0.495211i
$477$	2.98357			0.136608
$478$	2.26828	−	0.607785i	0.103749	−	0.0277994i
$479$	2.16985	−	2.82780i	0.0991429	−	0.129206i	−0.741147	−	0.671343i	$-0.765718\pi$
$479$	2.16985	−	2.82780i	0.0991429	−	0.129206i	0.840290	+	0.542137i	$0.182385\pi$
$480$	−0.712784	+	0.411526i	−0.0325340	+	0.0187835i
$481$	0.527816	−	4.00916i	0.0240664	−	0.182802i
$482$	3.94955	−	9.53506i	0.179897	−	0.434310i
$483$	−10.0265	−	3.50696i	−0.456220	−	0.159572i
$484$	−7.58613	+	7.58613i	−0.344824	+	0.344824i
$485$	−3.22521	−	12.0367i	−0.146449	−	0.546556i
$486$	−0.130526	−	0.991445i	−0.00592079	−	0.0449729i
$487$	−14.7577	+	1.94288i	−0.668734	+	0.0880404i	−0.457246	−	0.889340i	$-0.651164\pi$
$487$	−14.7577	+	1.94288i	−0.668734	+	0.0880404i	−0.211488	+	0.977381i	$0.567831\pi$
$488$	−1.91085	+	14.5144i	−0.0865003	+	0.657035i
$489$		−	3.36232i		−	0.152049i
$490$	2.97221	−	4.93552i	0.134271	−	0.222964i
$491$	1.36875	+	1.36875i	0.0617709	+	0.0617709i	0.737317	−	0.675547i	$-0.236092\pi$
$491$	1.36875	+	1.36875i	0.0617709	+	0.0617709i	−0.675547	+	0.737317i	$0.736092\pi$
$492$	2.23724	−	3.87501i	0.100862	−	0.174699i
$493$	0.202412	+	0.564854i	0.00911618	+	0.0254398i
$494$	−6.58677	−	11.4086i	−0.296353	−	0.513298i
$495$	−0.414316	+	0.111016i	−0.0186221	+	0.00498978i
$496$	1.84067	+	4.44377i	0.0826485	+	0.199531i
$497$	−0.319528	−	5.67669i	−0.0143328	−	0.254634i
$498$	−4.86152	+	2.01371i	−0.217850	+	0.0902364i
$499$	−25.0724	−	32.6750i	−1.12239	−	1.46273i	−0.868627	−	0.495467i	$-0.834997\pi$
$499$	−25.0724	−	32.6750i	−1.12239	−	1.46273i	−0.253767	−	0.967265i	$-0.581670\pi$
$500$	1.00152	+	7.60733i	0.0447895	+	0.340210i
$501$	−20.7271	−	5.55380i	−0.926017	−	0.248125i
$502$	−1.31926	−	4.92353i	−0.0588813	−	0.219748i
$503$	32.9055	+	13.6299i	1.46718	+	0.607727i	0.966215	−	0.257738i	$-0.0829771\pi$
$503$	32.9055	+	13.6299i	1.46718	+	0.607727i	0.500969	+	0.865465i	$0.332977\pi$
$504$	1.72605	+	2.00518i	0.0768843	+	0.0893179i
$505$	3.44927	−	1.42873i	0.153491	−	0.0635779i
$506$	−1.81197	−	1.04614i	−0.0805520	−	0.0465067i
$507$	−12.8156	+	16.7016i	−0.569161	+	0.741745i
$508$	2.24165	−	8.36596i	0.0994572	−	0.371179i
$509$	−4.53356	+	7.85235i	−0.200946	+	0.348049i	−0.948834	−	0.315776i	$-0.897735\pi$
$509$	−4.53356	+	7.85235i	−0.200946	+	0.348049i	0.747887	+	0.663826i	$0.231068\pi$
$510$	1.83757	−	2.85296i	0.0813688	−	0.126331i
$511$	3.55846	+	5.43341i	0.157417	+	0.240360i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.23821	−	0.294665i	−0.0988192	−	0.0130098i
$514$	−18.3979	+	10.6221i	−0.811499	+	0.468519i
$515$	7.57279	+	5.81081i	0.333697	+	0.256055i
$516$	−1.98334	−	2.58474i	−0.0873118	−	0.113787i
$517$	2.52824	+	1.04723i	0.111192	+	0.0460572i
$518$	1.79482	+	0.374250i	0.0788600	+	0.0164436i
$519$	10.3798	−	10.3798i	0.455622	−	0.455622i
$520$	3.81035	−	2.92378i	0.167095	−	0.128216i
$521$	36.0237	−	4.74261i	1.57823	−	0.207778i	0.710094	−	0.704107i	$-0.248653\pi$
$521$	36.0237	−	4.74261i	1.57823	−	0.207778i	0.868134	+	0.496330i	$0.165319\pi$
$522$	0.115455	+	0.0885916i	0.00505332	+	0.00387755i
$523$	18.9092	+	10.9172i	0.826843	+	0.477378i	0.852770	−	0.522286i	$-0.174921\pi$
$523$	18.9092	+	10.9172i	0.826843	+	0.477378i	−0.0259276	+	0.999664i	$0.508254\pi$
$524$	−6.74917	−	16.2939i	−0.294839	−	0.711804i
$525$	10.8630	−	3.57612i	0.474100	−	0.156075i
$526$	−23.6119			−1.02953
$527$	−15.1284	−	12.8231i	−0.659002	−	0.558581i
$528$	0.260573	+	0.451326i	0.0113400	+	0.0196415i
$529$	1.78109	−	6.64712i	0.0774387	−	0.289005i
$530$	2.43462	+	0.320524i	0.105753	+	0.0139227i
$531$		−	9.10163i		−	0.394977i
$532$	5.38100	−	2.59221i	0.233296	−	0.112386i
$533$	−9.99201	+	24.1228i	−0.432802	+	1.04488i
$534$	−2.56204	+	1.96592i	−0.110870	+	0.0850737i
$535$	−8.26676	−	2.21507i	−0.357403	−	0.0957659i
$536$	−1.74164	−	0.466671i	−0.0752275	−	0.0201571i
$537$	12.6786	−	9.72860i	0.547120	−	0.419820i
$538$	−6.57383	+	15.8706i	−0.283418	+	0.684231i
$539$	−3.12511	−	1.88197i	−0.134608	−	0.0810620i
$540$		−	0.823052i		−	0.0354185i
$541$	−8.14542	−	1.07236i	−0.350199	−	0.0461045i	−0.0466249	−	0.998912i	$-0.514847\pi$
$541$	−8.14542	−	1.07236i	−0.350199	−	0.0461045i	−0.303574	+	0.952808i	$0.598180\pi$
$542$	8.32797	−	31.0804i	0.357717	−	1.33502i
$543$	6.09047	+	10.5490i	0.261367	+	0.452701i
$544$	−3.92606	−	1.25940i	−0.168328	−	0.0539962i
$545$	9.42623			0.403775
$546$	−11.5133	−	10.2863i	−0.492724	−	0.440211i
$547$	−9.61793	−	23.2197i	−0.411233	−	0.992805i	−0.984807	−	0.173651i	$-0.944444\pi$
$547$	−9.61793	−	23.2197i	−0.411233	−	0.992805i	0.573574	−	0.819154i	$-0.305556\pi$
$548$	−6.66211	−	3.84637i	−0.284591	−	0.164309i
$549$	−11.6144	−	8.91203i	−0.495690	−	0.380356i
$550$	2.23343	−	0.294037i	0.0952338	−	0.0125378i
$551$	0.260641	−	0.199997i	0.0111037	−	0.00852017i
$552$	2.83887	−	2.83887i	0.120830	−	0.120830i
$553$	3.02653	+	9.19352i	0.128701	+	0.390948i
$554$	19.6404	+	8.13534i	0.834442	+	0.345637i
$555$	−0.347207	−	0.452489i	−0.0147381	−	0.0192071i
$556$	−8.14744	−	6.25175i	−0.345528	−	0.265133i
$557$	−1.79863	+	1.03844i	−0.0762104	+	0.0440001i	−0.537621	−	0.843187i	$-0.680677\pi$
$557$	−1.79863	+	1.03844i	−0.0762104	+	0.0440001i	0.461411	+	0.887187i	$0.347344\pi$
$558$	−4.76875	−	0.627818i	−0.201877	−	0.0265777i
$559$	13.4433	+	13.4433i	0.568592	+	0.568592i
$560$	1.19306	+	1.82168i	0.0504159	+	0.0769800i
$561$	−1.80646	−	1.16352i	−0.0762689	−	0.0491240i
$562$	−0.960358	+	1.66339i	−0.0405103	+	0.0701658i
$563$	9.69241	−	36.1726i	0.408486	−	1.52449i	−0.389048	−	0.921218i	$-0.627196\pi$
$563$	9.69241	−	36.1726i	0.408486	−	1.52449i	0.797534	−	0.603274i	$-0.206138\pi$
$564$	−3.19661	+	4.16591i	−0.134602	+	0.175416i
$565$	−6.31136	−	3.64387i	−0.265521	−	0.153299i
$566$	−17.3282	+	7.17758i	−0.728359	+	0.301696i
$567$	−2.59956	+	0.492210i	−0.109171	+	0.0206709i
$568$	1.98540	+	0.822380i	0.0833056	+	0.0345063i
$569$	−11.4593	−	42.7666i	−0.480398	−	1.79287i	−0.599946	−	0.800041i	$-0.704811\pi$
$569$	−11.4593	−	42.7666i	−0.480398	−	1.79287i	0.119548	−	0.992828i	$-0.461855\pi$
$570$	−1.79474	−	0.480900i	−0.0751736	−	0.0201427i
$571$	−3.84852	−	29.2324i	−0.161055	−	1.22334i	−0.860800	−	0.508944i	$-0.830036\pi$
$571$	−3.84852	−	29.2324i	−0.161055	−	1.22334i	0.699744	−	0.714393i	$-0.253297\pi$
$572$	−1.85131	−	2.41267i	−0.0774070	−	0.100879i
$573$	−17.8750	+	7.40405i	−0.746737	+	0.309309i
$574$	−10.5688	−	5.33365i	−0.441132	−	0.222622i
$575$	−6.64116	−	16.0332i	−0.276956	−	0.668630i
$576$	−0.965926	+	0.258819i	−0.0402469	+	0.0107841i
$577$	16.2624	+	28.1672i	0.677011	+	1.17262i	0.975877	+	0.218322i	$0.0700584\pi$
$577$	16.2624	+	28.1672i	0.677011	+	1.17262i	−0.298866	+	0.954295i	$0.596608\pi$
$578$	16.7703	−	2.78523i	0.697552	−	0.115850i
$579$	−2.34885	+	4.06833i	−0.0976148	+	0.169074i
$580$	0.0846950	+	0.0846950i	0.00351677	+	0.00351677i
$581$	6.04220	+	12.5426i	0.250673	+	0.520356i
$582$		−	15.1403i		−	0.627586i
$583$	0.202952	−	1.54157i	0.00840542	−	0.0638455i
$584$	−2.43386	+	0.320424i	−0.100714	+	0.0132592i
$585$	0.626897	+	4.76175i	0.0259190	+	0.196874i
$586$	1.64669	+	6.14555i	0.0680243	+	0.253870i
$587$	−25.6702	+	25.6702i	−1.05952	+	1.05952i	−0.0614094	+	0.998113i	$0.519560\pi$
$587$	−25.6702	+	25.6702i	−1.05952	+	1.05952i	−0.998113	+	0.0614094i	$0.980440\pi$
$588$	5.04019	−	4.85762i	0.207854	−	0.200325i
$589$	−4.15535	+	10.0319i	−0.171218	+	0.413357i
$590$	0.977787	−	7.42703i	0.0402548	−	0.305766i
$591$	−8.77582	+	5.06672i	−0.360989	+	0.208417i
$592$	−0.421853	+	0.549770i	−0.0173381	+	0.0225954i
$593$	12.9630	−	3.47343i	0.532328	−	0.142637i	0.0173650	−	0.999849i	$-0.494472\pi$
$593$	12.9630	−	3.47343i	0.532328	−	0.142637i	0.514963	+	0.857212i	$0.327806\pi$
$594$	−0.521147			−0.0213829
$595$	−7.80953	−	4.42985i	−0.320160	−	0.181606i
$596$	−23.0195			−0.942917
$597$	−14.1939	+	3.80325i	−0.580918	+	0.155657i
$598$	−14.2619	+	18.5865i	−0.583214	+	0.760060i
$599$	21.9454	−	12.6702i	0.896664	−	0.517689i	0.0205476	−	0.999789i	$-0.493459\pi$
$599$	21.9454	−	12.6702i	0.896664	−	0.517689i	0.876116	+	0.482100i	$0.160126\pi$
$600$	−0.564211	+	4.28560i	−0.0230338	+	0.174959i
$601$	6.00011	−	14.4856i	0.244750	−	0.590878i	−0.752993	−	0.658028i	$-0.771391\pi$
$601$	6.00011	−	14.4856i	0.244750	−	0.590878i	0.997743	+	0.0671502i	$0.0213907\pi$
$602$	−6.53288	+	5.62346i	−0.266260	+	0.229195i
$603$	1.27497	−	1.27497i	0.0519208	−	0.0519208i
$604$	−1.80054	−	6.71970i	−0.0732628	−	0.273421i
$605$	−1.15255	−	8.75450i	−0.0468579	−	0.355921i
$606$	4.49731	−	0.592082i	0.182691	−	0.0240517i
$607$	5.48546	−	41.6662i	0.222648	−	1.69118i	−0.406308	−	0.913736i	$-0.633184\pi$
$607$	5.48546	−	41.6662i	0.222648	−	1.69118i	0.628955	−	0.777441i	$-0.283483\pi$
$608$			2.25752i			0.0915545i
$609$	0.216854	−	0.318154i	0.00878737	−	0.0128923i
$610$	−8.52005	−	8.52005i	−0.344967	−	0.344967i
$611$	15.3209	−	26.5365i	0.619817	−	1.07355i
$612$	3.05370	−	2.77037i	0.123438	−	0.111985i
$613$	24.5322	+	42.4910i	0.990845	+	1.71619i	0.612338	+	0.790596i	$0.290229\pi$
$613$	24.5322	+	42.4910i	0.990845	+	1.71619i	0.378507	+	0.925598i	$0.376438\pi$
$614$	−20.0367	+	5.36882i	−0.808616	+	0.216668i
$615$	1.40932	+	3.40240i	0.0568292	+	0.137198i
$616$	1.15347	−	0.755430i	0.0464745	−	0.0304371i
$617$	−34.6802	+	14.3650i	−1.39617	+	0.578314i	−0.948755	−	0.316012i	$-0.897656\pi$
$617$	−34.6802	+	14.3650i	−1.39617	+	0.578314i	−0.447417	+	0.894325i	$0.647656\pi$
$618$	7.06007	+	9.20086i	0.283998	+	0.370113i
$619$	−6.12323	−	46.5105i	−0.246113	−	1.86942i	−0.453638	−	0.891186i	$-0.649874\pi$
$619$	−6.12323	−	46.5105i	−0.246113	−	1.86942i	0.207524	−	0.978230i	$-0.433459\pi$
$620$	−3.82391	−	1.02461i	−0.153572	−	0.0411495i
$621$	1.03910	+	3.87797i	0.0416976	+	0.155618i
$622$	−26.6419	−	11.0354i	−1.06824	−	0.442481i
$623$	5.57406	+	6.47549i	0.223320	+	0.259435i
$624$	5.39121	−	2.23311i	0.215821	−	0.0893960i
$625$	13.2482	+	7.64883i	0.529927	+	0.305953i
$626$	15.8203	−	20.6174i	0.632305	−	0.824036i
$627$	−0.304500	+	1.13641i	−0.0121606	+	0.0453839i
$628$	−2.11504	+	3.66335i	−0.0843992	+	0.146184i
$629$	0.510144	−	2.81128i	0.0203408	−	0.112093i
$630$	−2.17415	+	0.122378i	−0.0866202	+	0.00487566i
$631$	26.7440	+	26.7440i	1.06466	+	1.06466i	0.997760	+	0.0669005i	$0.0213110\pi$
$631$	26.7440	+	26.7440i	1.06466	+	1.06466i	0.0669005	+	0.997760i	$0.478689\pi$
$632$	−3.62697	−	0.477500i	−0.144273	−	0.0189939i
$633$	−1.85902	+	1.07330i	−0.0738893	+	0.0426600i
$634$	−14.1832	−	10.8831i	−0.563285	−	0.432224i
$635$	4.33957	+	5.65543i	0.172210	+	0.224429i
$636$	2.75646	+	1.14176i	0.109301	+	0.0452738i
$637$	−25.4600	+	31.9427i	−1.00876	+	1.26561i
$638$	0.0536279	−	0.0536279i	0.00212315	−	0.00212315i
$639$	−1.70490	+	1.30822i	−0.0674449	+	0.0517523i
$640$	−0.816011	+	0.107430i	−0.0322557	+	0.00424654i
$641$	−27.2151	−	20.8828i	−1.07493	−	0.824823i	−0.0896845	−	0.995970i	$-0.528586\pi$
$641$	−27.2151	−	20.8828i	−1.07493	−	0.824823i	−0.985245	+	0.171147i	$0.945253\pi$
$642$	−9.00523	−	5.19917i	−0.355408	−	0.205195i
$643$	5.93004	+	14.3164i	0.233858	+	0.564583i	0.996625	−	0.0820906i	$-0.0261597\pi$
$643$	5.93004	+	14.3164i	0.233858	+	0.564583i	−0.762767	+	0.646673i	$0.776160\pi$
$644$	−7.92119	−	7.07697i	−0.312138	−	0.278872i
$645$	2.68150			0.105584
$646$	−4.25681	−	8.27758i	−0.167482	−	0.325677i
$647$	−10.5367	−	18.2500i	−0.414239	−	0.717483i	0.581109	−	0.813825i	$-0.302619\pi$
$647$	−10.5367	−	18.2500i	−0.414239	−	0.717483i	−0.995348	+	0.0963428i	$0.969285\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−4.70270	−	0.619123i	−0.184597	−	0.0243027i
$650$		−	25.2240i		−	0.989368i
$651$	−0.949369	+	12.6903i	−0.0372087	+	0.497374i
$652$	1.28670	−	3.10638i	0.0503912	−	0.121655i
$653$	3.99259	−	3.06362i	0.156242	−	0.119889i	−0.527682	−	0.849442i	$-0.676939\pi$
$653$	3.99259	−	3.06362i	0.156242	−	0.119889i	0.683924	+	0.729553i	$0.260272\pi$
$654$	11.0625	+	2.96420i	0.432579	+	0.115909i
$655$	14.0211	+	3.75694i	0.547849	+	0.146796i
$656$	3.54984	−	2.72389i	0.138598	−	0.106350i
$657$	0.939436	−	2.26800i	0.0366509	−	0.0884831i
$658$	11.4798	+	7.82465i	0.447530	+	0.305037i
$659$			7.46366i			0.290743i	0.989377	+	0.145371i	$0.0464377\pi$
$659$			7.46366i			0.290743i	−0.989377	+	0.145371i	$0.953562\pi$
$660$	−0.425262	−	0.0559867i	−0.0165533	−	0.00217928i
$661$	3.14514	−	11.7378i	0.122332	−	0.456548i	−0.877399	−	0.479762i	$-0.840723\pi$
$661$	3.14514	−	11.7378i	0.122332	−	0.456548i	0.999731	+	0.0232138i	$0.00738984\pi$
$662$	−1.50483	−	2.60643i	−0.0584867	−	0.101302i
$663$	−15.5570	+	18.3538i	−0.604184	+	0.712803i
$664$	−5.26207			−0.204208
$665$	−1.00347	+	4.81245i	−0.0389131	+	0.186619i
$666$	−0.265188	−	0.640221i	−0.0102758	−	0.0248081i
$667$	−0.505984	−	0.292130i	−0.0195918	−	0.0113113i
$668$	−17.0240	−	13.0629i	−0.658677	−	0.505420i
$669$	−10.9458	+	1.44104i	−0.423188	+	0.0557138i
$670$	1.17736	−	0.903420i	0.0454854	−	0.0349021i
$671$	−5.39479	+	5.39479i	−0.208264	+	0.208264i
$672$	0.827310	+	2.51308i	0.0319142	+	0.0969441i
$673$	−15.9858	−	6.62155i	−0.616208	−	0.255242i	0.0526721	−	0.998612i	$-0.483226\pi$
$673$	−15.9858	−	6.62155i	−0.616208	−	0.255242i	−0.668880	+	0.743370i	$0.733226\pi$
$674$	10.9939	+	14.3275i	0.423468	+	0.551875i
$675$	−3.42934	−	2.63142i	−0.131995	−	0.101284i
$676$	−18.2315	+	10.5260i	−0.701212	+	0.404845i
$677$	11.2875	+	1.48603i	0.433816	+	0.0571129i	0.344272	−	0.938870i	$-0.388126\pi$
$677$	11.2875	+	1.48603i	0.433816	+	0.0571129i	0.0895437	+	0.995983i	$0.471459\pi$
$678$	−6.26109	−	6.26109i	−0.240456	−	0.240456i
$679$	−39.9942	+	2.25118i	−1.53484	+	0.0863925i
$680$	2.78947	−	1.93259i	0.106971	−	0.0741114i
$681$	2.03154	−	3.51873i	0.0778487	−	0.134838i
$682$	−0.648773	+	2.42125i	−0.0248428	+	0.0927146i
$683$	12.6380	−	16.4702i	0.483580	−	0.630213i	−0.486302	−	0.873791i	$-0.661654\pi$
$683$	12.6380	−	16.4702i	0.483580	−	0.630213i	0.969881	+	0.243578i	$0.0783211\pi$
$684$	−1.95507	−	1.12876i	−0.0747539	−	0.0431592i
$685$	5.84957	−	2.42297i	0.223500	−	0.0925769i
$686$	−13.5812	−	12.5917i	−0.518531	−	0.480755i
$687$	−22.0863	−	9.14845i	−0.842645	−	0.349035i
$688$	−0.843231	−	3.14698i	−0.0321479	−	0.119978i
$689$	−16.8171	−	4.50612i	−0.640679	−	0.171670i
$690$	0.431306	+	3.27610i	0.0164196	+	0.124719i
$691$	7.61635	+	9.92582i	0.289740	+	0.377596i	0.915431	−	0.402474i	$-0.131850\pi$
$691$	7.61635	+	9.92582i	0.289740	+	0.377596i	−0.625692	+	0.780071i	$0.715183\pi$
$692$	13.5618	−	5.61749i	0.515543	−	0.213545i
$693$	0.0774884	+	1.37665i	0.00294354	+	0.0522945i
$694$	3.31474	+	8.00249i	0.125826	+	0.303770i
$695$	8.16443	−	2.18765i	0.309694	−	0.0829824i
$696$	0.0727638	+	0.126031i	0.00275810	+	0.00477718i
$697$	−7.87989	+	16.6812i	−0.298472	+	0.631846i
$698$	5.29056	−	9.16351i	0.200251	−	0.346844i
$699$	9.23059	+	9.23059i	0.349133	+	0.349133i
$700$	11.4046	+	0.853183i	0.431054	+	0.0322473i
$701$			25.6627i			0.969267i	0.874717	+	0.484634i	$0.161047\pi$
$701$			25.6627i			0.969267i	−0.874717	+	0.484634i	$0.838953\pi$
$702$	−0.761673	+	5.78548i	−0.0287475	+	0.218359i
$703$	−1.55101	+	0.204194i	−0.0584974	+	0.00770133i
$704$	0.0680233	+	0.516688i	0.00256373	+	0.0194734i
$705$	−1.11858	−	4.17459i	−0.0421281	−	0.157224i
$706$	−13.3507	+	13.3507i	−0.502461	+	0.502461i
$707$	−2.23272	−	11.7919i	−0.0839702	−	0.443481i
$708$	3.48304	−	8.40881i	0.130901	−	0.316022i
$709$	−0.690698	+	5.24637i	−0.0259397	+	0.197032i	−0.999508	−	0.0313644i	$-0.990015\pi$
$709$	−0.690698	+	5.24637i	−0.0259397	+	0.197032i	0.973568	+	0.228396i	$0.0733481\pi$
$710$	−1.53176	+	0.884362i	−0.0574859	+	0.0331895i
$711$	2.22701	−	2.90230i	0.0835196	−	0.108845i
$712$	−3.11934	+	0.835825i	−0.116902	+	0.0313239i
$713$	19.3107			0.723190
$714$	−7.77216	−	7.65464i	−0.290866	−	0.286468i
$715$	2.50299			0.0936064
$716$	15.4364	−	4.13618i	0.576886	−	0.154576i
$717$	−1.42955	+	1.86303i	−0.0533877	+	0.0695762i
$718$	16.3899	−	9.46269i	0.611664	−	0.353145i
$719$	−3.36103	+	25.5296i	−0.125345	+	0.952092i	0.807007	+	0.590542i	$0.201086\pi$
$719$	−3.36103	+	25.5296i	−0.125345	+	0.952092i	−0.932352	+	0.361551i	$0.882247\pi$
$720$	0.314968	−	0.760401i	0.0117382	−	0.0283385i
$721$	23.2550	−	20.0177i	0.866060	−	0.745499i
$722$	9.83134	−	9.83134i	0.365884	−	0.365884i
$723$	2.67119	+	9.96900i	0.0993425	+	0.370751i
$724$	1.58993	+	12.0767i	0.0590893	+	0.448828i
$725$	0.623674	−	0.0821082i	0.0231627	−	0.00304942i
$726$	1.40034	−	10.6366i	0.0519714	−	0.394762i
$727$		−	22.7877i		−	0.845148i	−0.906328	−	0.422574i	$-0.861127\pi$
$727$		−	22.7877i		−	0.845148i	0.906328	−	0.422574i	$-0.138873\pi$
$728$	−6.70053	−	13.9092i	−0.248338	−	0.515510i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	1.01024	−	1.74979i	0.0373907	−	0.0647626i
$731$	9.02584	+	9.94894i	0.333833	+	0.367975i
$732$	−7.31981	−	12.6783i	−0.270548	−	0.468603i
$733$	−38.6752	+	10.3630i	−1.42850	+	0.382766i	−0.888491	−	0.458894i	$-0.848246\pi$
$733$	−38.6752	+	10.3630i	−1.42850	+	0.382766i	−0.540009	+	0.841659i	$0.681579\pi$
$734$	3.64391	+	8.79717i	0.134499	+	0.324709i
$735$	0.646541	+	5.72497i	0.0238480	+	0.211169i
$736$	3.70917	−	1.53639i	0.136722	−	0.0566320i
$737$	−0.572034	−	0.745490i	−0.0210712	−	0.0274605i
$738$	0.584036	+	4.43620i	0.0214987	+	0.163299i
$739$	8.83729	+	2.36795i	0.325085	+	0.0871063i	0.417671	−	0.908598i	$-0.362847\pi$
$739$	8.83729	+	2.36795i	0.325085	+	0.0871063i	−0.0925857	+	0.995705i	$0.529513\pi$
$740$	−0.147618	−	0.550916i	−0.00542653	−	0.0202521i
$741$	12.1708	+	5.04129i	0.447104	+	0.185197i
$742$	2.60619	−	7.45114i	0.0956763	−	0.273540i
$743$	−6.54720	+	2.71194i	−0.240193	+	0.0994914i	−0.499533	−	0.866295i	$-0.666495\pi$
$743$	−6.54720	+	2.71194i	−0.240193	+	0.0994914i	0.259340	+	0.965786i	$0.416495\pi$
$744$	−4.16550	−	2.40495i	−0.152715	−	0.0881698i
$745$	11.5338	−	15.0311i	0.422564	−	0.550697i
$746$	8.52591	−	31.8191i	0.312156	−	1.16498i
$747$	2.63104	−	4.55709i	0.0962646	−	0.166735i
$748$	−1.22369	−	1.76626i	−0.0447426	−	0.0645809i
$749$	−12.3950	+	24.5610i	−0.452904	+	0.897439i
$750$	−5.42561	−	5.42561i	−0.198115	−	0.198115i
$751$	28.6338	+	3.76971i	1.04486	+	0.137559i	0.633366	−	0.773852i	$-0.281673\pi$
$751$	28.6338	+	3.76971i	1.04486	+	0.137559i	0.411497	+	0.911411i	$0.365006\pi$
$752$	−4.54751	+	2.62551i	−0.165831	+	0.0957423i
$753$	4.04389	+	3.10299i	0.147368	+	0.113079i
$754$	−0.516968	−	0.673725i	−0.0188269	−	0.0245356i
$755$	5.28991	+	2.19115i	0.192520	+	0.0797443i
$756$	−2.59004	−	0.540067i	−0.0941990	−	0.0196420i
$757$	26.9319	−	26.9319i	0.978858	−	0.978858i	−0.0209233	−	0.999781i	$-0.506661\pi$
$757$	26.9319	−	26.9319i	0.978858	−	0.978858i	0.999781	+	0.0209233i	$0.00666058\pi$
$758$	−20.6384	+	15.8364i	−0.749622	+	0.575205i
$759$	2.07439	−	0.273098i	0.0752954	−	0.00991283i
$760$	−1.47409	−	1.13111i	−0.0534710	−	0.0410298i
$761$	−13.9349	−	8.04533i	−0.505140	−	0.291643i	0.225693	−	0.974198i	$-0.427535\pi$
$761$	−13.9349	−	8.04533i	−0.505140	−	0.291643i	−0.730834	+	0.682555i	$0.760869\pi$
$762$	3.31445	+	8.00179i	0.120070	+	0.289874i
$763$	6.18526	−	29.6632i	0.223922	−	1.07388i
$764$	−19.3477			−0.699976
$765$	0.278937	+	3.38205i	0.0100850	+	0.122278i
$766$	−16.1741	−	28.0144i	−0.584394	−	1.01220i
$767$	−13.7463	+	51.3019i	−0.496350	+	1.85241i
$768$	−0.991445	−	0.130526i	−0.0357757	−	0.00470996i
$769$			16.8986i			0.609379i	0.952452	+	0.304690i	$0.0985527\pi$
$769$			16.8986i			0.609379i	−0.952452	+	0.304690i	$0.901447\pi$
$770$	−0.0846615	+	1.13168i	−0.00305099	+	0.0407830i
$771$	8.12977	−	19.6270i	0.292787	−	0.706849i
$772$	−3.72693	+	2.85978i	−0.134135	+	0.102926i
$773$	41.3467	+	11.0788i	1.48714	+	0.398477i	0.908769	−	0.417300i	$-0.137024\pi$
$773$	41.3467	+	11.0788i	1.48714	+	0.398477i	0.578367	+	0.815777i	$0.303690\pi$
$774$	3.14698	+	0.843231i	0.113116	+	0.0303093i
$775$	−16.4948	+	12.6569i	−0.592510	+	0.454649i
$776$	5.79395	−	13.9878i	0.207991	−	0.502134i
$777$	−1.65176	+	0.795706i	−0.0592565	+	0.0285458i
$778$			30.4931i			1.09323i
$779$	10.0148	+	1.31847i	0.358817	+	0.0472392i
$780$	−1.24307	+	4.63919i	−0.0445089	+	0.166110i
$781$	0.559968	+	0.969892i	0.0200372	+	0.0347055i
$782$	−10.7033	+	12.6275i	−0.382748	+	0.451557i
$783$	−0.145528			−0.00520073
$784$	6.51546	−	2.55906i	0.232695	−	0.0913951i
$785$	−1.33234	−	3.21655i	−0.0475533	−	0.114804i
$786$	15.2736	+	8.81821i	0.544791	+	0.314535i
$787$	−6.06811	−	4.65622i	−0.216305	−	0.165976i	0.494926	−	0.868935i	$-0.335195\pi$
$787$	−6.06811	−	4.65622i	−0.216305	−	0.165976i	−0.711231	+	0.702959i	$0.751862\pi$
$788$	−10.0468	+	1.32268i	−0.357901	+	0.0471185i
$789$	18.7326	−	14.3740i	0.666899	−	0.511729i
$790$	2.12906	−	2.12906i	0.0757486	−	0.0757486i
$791$	−15.6082	+	17.4701i	−0.554963	+	0.621164i
$792$	−0.481477	−	0.199434i	−0.0171085	−	0.00708659i
$793$	52.0053	+	67.7746i	1.84676	+	2.40675i
$794$	13.9501	+	10.7043i	0.495072	+	0.379882i
$795$	−2.12664	+	1.22782i	−0.0754241	+	0.0435461i
$796$	−14.5689	−	1.91803i	−0.516381	−	0.0679829i
$797$	−27.1246	−	27.1246i	−0.960801	−	0.960801i	0.0384591	−	0.999260i	$-0.487755\pi$
$797$	−27.1246	−	27.1246i	−0.960801	−	0.960801i	−0.999260	+	0.0384591i	$0.987755\pi$
$798$	−2.69100	+	5.33228i	−0.0952604	+	0.188761i
$799$	11.7235	−	18.2017i	0.414749	−	0.643930i
$800$	−2.16129	+	3.74347i	−0.0764132	+	0.132352i
$801$	0.835825	−	3.11934i	0.0295324	−	0.110216i
$802$	−17.4237	+	22.7070i	−0.615252	+	0.801812i
$803$	−1.10795	−	0.639672i	−0.0390985	−	0.0225735i
$804$	1.66583	−	0.690009i	0.0587492	−	0.0243347i
$805$	8.58991	−	1.62644i	0.302755	−	0.0573246i
$806$	25.9312	+	10.7411i	0.913387	+	0.378337i
$807$	−4.44606	−	16.5929i	−0.156509	−	0.584098i
$808$	4.38156	+	1.17403i	0.154143	+	0.0413024i
$809$	3.88421	+	29.5035i	0.136561	+	1.03729i	0.913249	+	0.407401i	$0.133565\pi$
$809$	3.88421	+	29.5035i	0.136561	+	1.03729i	−0.776688	+	0.629886i	$0.783102\pi$
$810$	0.501042	+	0.652971i	0.0176048	+	0.0229431i
$811$	38.4155	−	15.9122i	1.34895	−	0.558754i	0.412950	−	0.910754i	$-0.364498\pi$
$811$	38.4155	−	15.9122i	1.34895	−	0.558754i	0.936000	+	0.352000i	$0.114498\pi$
$812$	0.322100	−	0.210950i	0.0113035	−	0.00740289i
$813$	12.3135	+	29.7275i	0.431854	+	1.04259i
$814$	−0.348834	+	0.0934697i	−0.0122266	+	0.00327611i
$815$	1.38368	+	2.39661i	0.0484683	+	0.0839495i
$816$	3.88142	−	1.39088i	0.135877	−	0.0486907i
$817$	3.67749	−	6.36961i	0.128659	−	0.222844i
$818$	−15.6685	−	15.6685i	−0.547836	−	0.547836i
$819$	15.3960	+	1.15178i	0.537980	+	0.0402464i
$820$			3.68273i			0.128606i
$821$	1.92533	−	14.6243i	0.0671944	−	0.510393i	−0.924441	−	0.381324i	$-0.875468\pi$
$821$	1.92533	−	14.6243i	0.0671944	−	0.510393i	0.991636	−	0.129068i	$-0.0411986\pi$
$822$	7.62692	−	1.00410i	0.266020	−	0.0350221i
$823$	−1.98703	−	15.0930i	−0.0692634	−	0.526107i	−0.990543	−	0.137206i	$-0.956188\pi$
$823$	−1.98703	−	15.0930i	−0.0692634	−	0.526107i	0.921279	−	0.388902i	$-0.127145\pi$
$824$	3.00164	+	11.2023i	0.104567	+	0.390249i
$825$	−1.59290	+	1.59290i	−0.0554577	+	0.0554577i
$826$	−22.7303	−	7.95041i	−0.790890	−	0.276630i
$827$	−14.3792	+	34.7144i	−0.500013	+	1.20714i	0.449464	+	0.893299i	$0.351615\pi$
$827$	−14.3792	+	34.7144i	−0.500013	+	1.20714i	−0.949476	+	0.313839i	$0.898385\pi$
$828$	−0.524033	+	3.98042i	−0.0182114	+	0.138329i
$829$	−3.32147	+	1.91765i	−0.115359	+	0.0666027i	−0.556569	−	0.830801i	$-0.687883\pi$
$829$	−3.32147	+	1.91765i	−0.115359	+	0.0666027i	0.441210	+	0.897404i	$0.354549\pi$
$830$	2.63652	−	3.43598i	0.0915150	−	0.119265i
$831$	−20.5343	+	5.50215i	−0.712326	+	0.190867i
$832$	5.83540			0.202306
$833$	−19.0646	+	21.6689i	−0.660550	+	0.750782i
$834$	10.2696			0.355608
$835$	17.0595	−	4.57107i	0.590367	−	0.158188i
$836$	−0.716207	+	0.933379i	−0.0247705	+	0.0322816i
$837$	4.16550	−	2.40495i	0.143981	−	0.0831273i
$838$	−2.20714	+	16.7649i	−0.0762442	+	0.579132i
$839$	−5.02073	+	12.1211i	−0.173335	+	0.418467i	−0.986542	−	0.163507i	$-0.947719\pi$
$839$	−5.02073	+	12.1211i	−0.173335	+	0.418467i	0.813207	+	0.581974i	$0.197719\pi$
$840$	−2.05548	−	0.718949i	−0.0709210	−	0.0248061i
$841$	−20.4911	+	20.4911i	−0.706590	+	0.706590i
$842$	6.55137	+	24.4500i	0.225775	+	0.842604i
$843$	−0.250704	−	1.90428i	−0.00863469	−	0.0655870i
$844$	−2.12824	+	0.280189i	−0.0732572	+	0.00964449i
$845$	2.26161	−	17.1786i	0.0778016	−	0.590962i
$846$		−	5.25101i		−	0.180533i
$847$	−28.3056	−	2.11755i	−0.972592	−	0.0727599i
$848$	2.10970	+	2.10970i	0.0724474	+	0.0724474i
$849$	9.37797	−	16.2431i	0.321851	−	0.557462i
$850$	0.866015	−	17.8014i	0.0297041	−	0.610584i
$851$	1.39106	+	2.40938i	0.0476849	+	0.0825926i
$852$	−2.07576	+	0.556197i	−0.0711143	+	0.0190550i
$853$	−15.1148	−	36.4904i	−0.517521	−	1.24941i	−0.939421	−	0.342765i	$-0.888637\pi$
$853$	−15.1148	−	36.4904i	−0.517521	−	1.24941i	0.421900	−	0.906642i	$-0.361363\pi$
$854$	−32.4022	+	21.2209i	−1.10878	+	0.726164i
$855$	1.71662	−	0.711047i	0.0587072	−	0.0243173i
$856$	−6.33011	−	8.24956i	−0.216359	−	0.281964i
$857$	−6.02368	−	45.7544i	−0.205765	−	1.56294i	−0.713019	−	0.701144i	$-0.752673\pi$
$857$	−6.02368	−	45.7544i	−0.205765	−	1.56294i	0.507254	−	0.861796i	$-0.330660\pi$
$858$	2.93748	+	0.787095i	0.100284	+	0.0268710i
$859$	2.81636	+	10.5108i	0.0960931	+	0.358624i	0.997183	−	0.0750082i	$-0.0238983\pi$
$859$	2.81636	+	10.5108i	0.0960931	+	0.358624i	−0.901090	+	0.433632i	$0.857232\pi$
$860$	2.47738	+	1.02617i	0.0844781	+	0.0349920i
$861$	11.6317	−	2.20238i	0.396407	−	0.0750570i
$862$	22.3567	−	9.26046i	0.761474	−	0.315413i
$863$	−28.2127	−	16.2886i	−0.960372	−	0.554471i	−0.0640846	−	0.997944i	$-0.520413\pi$
$863$	−28.2127	−	16.2886i	−0.960372	−	0.554471i	−0.896288	+	0.443473i	$0.853746\pi$
$864$	0.608761	−	0.793353i	0.0207105	−	0.0269904i
$865$	−3.12699	+	11.6701i	−0.106321	+	0.396795i
$866$	1.07712	−	1.86563i	0.0366020	−	0.0633966i
$867$	−11.6092	+	12.4188i	−0.394270	+	0.421764i
$868$	−5.73349	+	11.3610i	−0.194607	+	0.385619i
$869$	−1.34810	−	1.34810i	−0.0457310	−	0.0457310i
$870$	−0.118752	−	0.0156340i	−0.00402607	−	0.000530043i
$871$	−9.11206	+	5.26085i	−0.308750	+	0.178257i
$872$	9.08610	+	6.97201i	0.307694	+	0.236102i
$873$	9.21684	+	12.0116i	0.311943	+	0.406532i
$874$	8.37351	+	3.46842i	0.283238	+	0.117321i
$875$	−13.5254	+	15.1389i	−0.457242	+	0.511787i
$876$	1.73585	−	1.73585i	0.0586490	−	0.0586490i
$877$	−29.2698	+	22.4595i	−0.988372	+	0.758404i	−0.970417	−	0.241435i	$-0.922382\pi$
$877$	−29.2698	+	22.4595i	−0.988372	+	0.758404i	−0.0179546	+	0.999839i	$0.505715\pi$
$878$	12.4373	−	1.63740i	0.419738	−	0.0552596i
$879$	−5.04758	−	3.87315i	−0.170251	−	0.130638i
$880$	−0.371465	−	0.214466i	−0.0125221	−	0.00722963i
$881$	5.30389	+	12.8047i	0.178693	+	0.431402i	0.987693	−	0.156406i	$-0.0499909\pi$
$881$	5.30389	+	12.8047i	0.178693	+	0.431402i	−0.809000	+	0.587808i	$0.799991\pi$
$882$	−1.04152	+	6.92208i	−0.0350697	+	0.233079i
$883$	4.41942			0.148725			0.0743626	−	0.997231i	$-0.476308\pi$
$883$	4.41942			0.148725			0.0743626	+	0.997231i	$0.476308\pi$
$884$	−21.3965	+	11.0033i	−0.719642	+	0.370081i
$885$	3.74556	+	6.48749i	0.125906	+	0.218075i
$886$	1.97611	−	7.37496i	0.0663889	−	0.247767i
$887$	−58.8083	−	7.74226i	−1.97459	−	0.259959i	−0.999225	−	0.0393534i	$-0.987470\pi$
$887$	−58.8083	−	7.74226i	−1.97459	−	0.259959i	−0.975363	−	0.220606i	$-0.929196\pi$
$888$		−	0.692970i		−	0.0232545i
$889$	20.6445	−	9.94512i	0.692393	−	0.333549i
$890$	1.01715	−	2.45562i	0.0340950	−	0.0823127i
$891$	0.413454	−	0.317254i	0.0138512	−	0.0106284i
$892$	−10.6640	−	2.85742i	−0.357059	−	0.0956736i
$893$	−11.4503	−	3.06811i	−0.383171	−	0.102670i
$894$	18.2626	−	14.0134i	0.610794	−	0.468678i
$895$	−5.03350	+	12.1519i	−0.168251	+	0.406195i
$896$	−0.197378	+	2.63838i	−0.00659393	+	0.0881420i
$897$		−	23.4278i		−	0.782232i
$898$	8.19359	+	1.07871i	0.273424	+	0.0359969i
$899$	−0.181167	+	0.676123i	−0.00604224	+	0.0225500i
$900$	−2.16129	−	3.74347i	−0.0720431	−	0.124782i
$901$	−11.7137	−	3.75750i	−0.390238	−	0.125180i
$902$	2.33186			0.0776424
$903$	1.75954	−	8.43835i	0.0585537	−	0.280811i
$904$	−3.38848	−	8.18051i	−0.112699	−	0.272080i
$905$	−8.68238	−	5.01277i	−0.288612	−	0.166630i
$906$	5.51915	+	4.23500i	0.183362	+	0.140698i
$907$	23.8124	−	3.13496i	0.790678	−	0.104095i	0.275639	−	0.961261i	$-0.411111\pi$
$907$	23.8124	−	3.13496i	0.790678	−	0.104095i	0.515039	+	0.857167i	$0.327777\pi$
$908$	3.22346	−	2.47345i	0.106974	−	0.0820842i
$909$	−3.20752	+	3.20752i	−0.106387	+	0.106387i
$910$	12.4396	+	2.59386i	0.412368	+	0.0859855i
$911$	48.1503	+	19.9445i	1.59529	+	0.660791i	0.990740	−	0.135776i	$-0.0433528\pi$
$911$	48.1503	+	19.9445i	1.59529	+	0.660791i	0.604550	+	0.796567i	$0.293353\pi$
$912$	−1.37429	−	1.79101i	−0.0455073	−	0.0593063i
$913$	−2.17562	−	1.66941i	−0.0720026	−	0.0552496i
$914$	−26.4579	+	15.2755i	−0.875150	+	0.505268i
$915$	11.9461	+	1.57273i	0.394925	+	0.0519929i
$916$	−16.9041	−	16.9041i	−0.558528	−	0.558528i
$917$	21.0229	−	41.6574i	0.694238	−	1.37565i
$918$	−0.736170	+	4.05685i	−0.0242972	+	0.133896i
$919$	10.7640	−	18.6438i	0.355071	−	0.615001i	−0.632059	−	0.774920i	$-0.717790\pi$
$919$	10.7640	−	18.6438i	0.355071	−	0.615001i	0.987130	+	0.159919i	$0.0511233\pi$
$920$	−0.855233	+	3.19177i	−0.0281962	+	0.105230i
$921$	12.6279	−	16.4570i	0.416102	−	0.542275i
$922$	−3.10145	−	1.79063i	−0.102141	−	0.0589711i
$923$	11.5856	−	4.79892i	0.381345	−	0.157958i
$924$	−0.455230	+	1.30151i	−0.0149760	+	0.0428165i
$925$	−2.76741	−	1.14630i	−0.0909918	−	0.0376901i
$926$	−5.44091	−	20.3058i	−0.178799	−	0.667289i
$927$	−11.2023	−	3.00164i	−0.367930	−	0.0985867i
$928$	0.0189952	+	0.144283i	0.000623547	+	0.00473631i
$929$	−4.38377	−	5.71305i	−0.143827	−	0.187439i	0.715885	−	0.698218i	$-0.246024\pi$
$929$	−4.38377	−	5.71305i	−0.143827	−	0.187439i	−0.859712	+	0.510779i	$0.829357\pi$
$930$	3.65746	−	1.51497i	0.119933	−	0.0496778i
$931$	14.4857	+	6.31562i	0.474750	+	0.206986i
$932$	4.99556	+	12.0603i	0.163635	+	0.395050i
$933$	27.8544	−	7.46356i	0.911912	−	0.244346i
$934$	−13.3269	−	23.0828i	−0.436068	−	0.755292i
$935$	1.76644	+	0.0859349i	0.0577687	+	0.00281037i
$936$	−2.91770	+	5.05361i	−0.0953681	+	0.165182i
$937$	33.9519	+	33.9519i	1.10916	+	1.10916i	0.993261	+	0.115899i	$0.0369750\pi$
$937$	33.9519	+	33.9519i	1.10916	+	1.10916i	0.115899	+	0.993261i	$0.463025\pi$
$938$	−2.07040	−	4.29781i	−0.0676008	−	0.140328i
$939$			25.9876i			0.848074i
$940$	0.564115	−	4.28488i	0.0183994	−	0.139757i
$941$	22.5001	−	2.96219i	0.733482	−	0.0965647i	0.245473	−	0.969403i	$-0.421057\pi$
$941$	22.5001	−	2.96219i	0.733482	−	0.0965647i	0.488009	+	0.872839i	$0.337723\pi$
$942$	−0.552136	−	4.19389i	−0.0179896	−	0.136644i
$943$	−4.64943	−	17.3519i	−0.151406	−	0.565055i
$944$	6.43582	−	6.43582i	0.209468	−	0.209468i
$945$	1.65037	−	1.42063i	0.0536865	−	0.0462130i
$946$	0.649756	−	1.56865i	0.0211254	−	0.0510012i
$947$	0.768850	−	5.83999i	0.0249843	−	0.189774i	−0.974402	−	0.224814i	$-0.927822\pi$
$947$	0.768850	−	5.83999i	0.0249843	−	0.189774i	0.999386	+	0.0350399i	$0.0111558\pi$
$948$	3.16816	−	1.82914i	0.102897	−	0.0594076i
$949$	−8.72058	+	11.3649i	−0.283082	+	0.368920i
$950$	−9.42581	+	2.52564i	−0.305814	+	0.0819425i
$951$	17.8775			0.579717
$952$	−4.25124	−	10.0462i	−0.137783	−	0.325601i
$953$	−5.11357			−0.165645			−0.0828225	−	0.996564i	$-0.526393\pi$
$953$	−5.11357			−0.165645			−0.0828225	+	0.996564i	$0.526393\pi$
$954$	−2.88190	+	0.772204i	−0.0933051	+	0.0250010i
$955$	9.69403	−	12.6335i	0.313691	−	0.408811i
$956$	−2.03369	+	1.17415i	−0.0657742	+	0.0379747i
$957$	−0.00989927	+	0.0751924i	−0.000319998	+	0.00243063i
$958$	−1.36402	+	3.29304i	−0.0440696	+	0.106393i
$959$	−3.78644	−	19.9978i	−0.122271	−	0.645761i
$960$	0.581986	−	0.581986i	0.0187835	−	0.0187835i
$961$	2.03557	+	7.59684i	0.0656634	+	0.245059i
$962$	0.527816	+	4.00916i	0.0170175	+	0.129261i
$963$	10.3094	−	1.35726i	0.332215	−	0.0437370i
$964$	−1.34712	+	10.2324i	−0.0433877	+	0.329563i
$965$		−	3.86645i		−	0.124465i
$966$	10.5925	+	0.792428i	0.340808	+	0.0254959i
$967$	4.47884	+	4.47884i	0.144030	+	0.144030i	0.775445	−	0.631415i	$-0.217526\pi$
$967$	4.47884	+	4.47884i	0.144030	+	0.144030i	−0.631415	+	0.775445i	$0.717526\pi$
$968$	5.36420	−	9.29107i	0.172412	−	0.298626i
$969$	8.41622	+	3.97566i	0.270368	+	0.127717i
$970$	6.23063	+	10.7918i	0.200054	+	0.346503i
$971$	−52.5153	+	14.0714i	−1.68530	+	0.451574i	−0.969169	−	0.246396i	$-0.920754\pi$
$971$	−52.5153	+	14.0714i	−1.68530	+	0.451574i	−0.716127	+	0.697970i	$0.754087\pi$
$972$	0.382683	+	0.923880i	0.0122746	+	0.0296334i
$973$	−1.52697	−	27.1279i	−0.0489525	−	0.869682i
$974$	13.7520	−	5.69625i	0.440641	−	0.182519i
$975$	15.3554	+	20.0116i	0.491767	+	0.640883i
$976$	−1.91085	−	14.5144i	−0.0611649	−	0.464594i
$977$	17.2414	+	4.61981i	0.551600	+	0.147801i	0.523844	−	0.851814i	$-0.324497\pi$
$977$	17.2414	+	4.61981i	0.551600	+	0.147801i	0.0277556	+	0.999615i	$0.491164\pi$
$978$	0.870232	+	3.24775i	0.0278270	+	0.103852i
$979$	−1.55487	−	0.644049i	−0.0496939	−	0.0205839i
$980$	−1.59353	+	5.53661i	−0.0509033	+	0.176860i
$981$	−10.5810	+	4.38279i	−0.337825	+	0.139932i
$982$	−1.67637	−	0.967853i	−0.0534951	−	0.0308854i
$983$	−0.460011	+	0.599498i	−0.0146721	+	0.0191210i	−0.800632	−	0.599157i	$-0.795503\pi$
$983$	−0.460011	+	0.599498i	−0.0146721	+	0.0191210i	0.785960	+	0.618278i	$0.212169\pi$
$984$	−1.15808	+	4.32201i	−0.0369182	+	0.137781i
$985$	4.17018	−	7.22296i	0.132873	−	0.230143i
$986$	−0.341710	−	0.493219i	−0.0108823	−	0.0157073i
$987$	−13.8709	+	0.780763i	−0.441516	+	0.0248520i
$988$	9.31509	+	9.31509i	0.296353	+	0.296353i
$989$	−12.9682	−	1.70730i	−0.412365	−	0.0542889i
$990$	0.371465	−	0.214466i	0.0118059	−	0.00681616i
$991$	−7.00177	−	5.37265i	−0.222419	−	0.170668i	0.491542	−	0.870854i	$-0.336434\pi$
$991$	−7.00177	−	5.37265i	−0.222419	−	0.170668i	−0.713960	+	0.700186i	$0.753100\pi$
$992$	−2.92808	−	3.81595i	−0.0929668	−	0.121157i
$993$	2.78055	+	1.15174i	0.0882382	+	0.0365495i
$994$	1.77788	+	5.40056i	0.0563908	+	0.171295i
$995$	8.55206	−	8.55206i	0.271118	−	0.271118i
$996$	4.17468	−	3.20335i	0.132280	−	0.101502i
$997$	41.4702	−	5.45966i	1.31338	−	0.172909i	0.558899	−	0.829236i	$-0.311224\pi$
$997$	41.4702	−	5.45966i	1.31338	−	0.172909i	0.754477	+	0.656327i	$0.227891\pi$
$998$	32.6750	+	25.0724i	1.03431	+	0.793652i
$999$	0.600130	+	0.346485i	0.0189873	+	0.0109623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bh.b.457.8	yes	96
7.4	even	3	inner	714.2.bh.b.151.2	yes	96
17.8	even	8	inner	714.2.bh.b.331.2	yes	96
119.25	even	24	inner	714.2.bh.b.25.8	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bh.b.25.8	✓	96	119.25	even	24	inner
714.2.bh.b.151.2	yes	96	7.4	even	3	inner
714.2.bh.b.331.2	yes	96	17.8	even	8	inner
714.2.bh.b.457.8	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.608761 - 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.107430 + 0.816011i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(2.49739 + 0.873515i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.107430 - 0.816011i) q^{10} +(-0.516688 + 0.0680233i) q^{11} +(0.130526 - 0.991445i) q^{12} +5.83540i q^{13} +(-2.63838 - 0.197378i) q^{14} +(0.581986 + 0.581986i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.200347 + 4.11824i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.18060 - 0.584289i) q^{19} +(0.314968 + 0.760401i) q^{20} +(2.21332 - 1.44955i) q^{21} +(0.481477 - 0.199434i) q^{22} +(-2.44404 - 3.18513i) q^{23} +(0.130526 + 0.991445i) q^{24} +(4.17530 + 1.11877i) q^{25} +(-1.51031 - 5.63657i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(2.59956 - 0.492210i) q^{28} +(0.134450 - 0.0556910i) q^{29} +(-0.712784 - 0.411526i) q^{30} +(-2.92808 + 3.81595i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.260573 + 0.451326i) q^{33} +(-0.872358 - 4.02976i) q^{34} +(-0.981092 + 1.94406i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(-0.687042 - 0.0904507i) q^{37} +(-1.95507 + 1.12876i) q^{38} +(4.62954 + 3.55237i) q^{39} +(-0.501042 - 0.652971i) q^{40} +(4.13388 + 1.71231i) q^{41} +(-1.76273 + 1.97301i) q^{42} +(2.30375 - 2.30375i) q^{43} +(-0.413454 + 0.317254i) q^{44} +(0.816011 - 0.107430i) q^{45} +(3.18513 + 2.44404i) q^{46} +(-4.54751 - 2.62551i) q^{47} +(-0.382683 - 0.923880i) q^{48} +(5.47394 + 4.36302i) q^{49} -4.32259 q^{50} +(3.14525 + 2.66597i) q^{51} +(2.91770 + 5.05361i) q^{52} +(-0.772204 + 2.88190i) q^{53} +(0.991445 + 0.130526i) q^{54} -0.428931i q^{55} +(-2.38359 + 1.14825i) q^{56} +(0.863915 - 2.08568i) q^{57} +(-0.115455 + 0.0885916i) q^{58} +(8.79150 + 2.35567i) q^{59} +(0.795007 + 0.213022i) q^{60} +(11.6144 - 8.91203i) q^{61} +(1.84067 - 4.44377i) q^{62} +(0.197378 - 2.63838i) q^{63} -1.00000i q^{64} +(-4.76175 - 0.626897i) q^{65} +(0.134883 - 0.503389i) q^{66} +(0.901540 + 1.56151i) q^{67} +(1.88561 + 3.66667i) q^{68} -4.01477 q^{69} +(0.444503 - 2.13174i) q^{70} +(-0.822380 - 1.98540i) q^{71} +(0.866025 + 0.500000i) q^{72} +(1.94757 + 1.49443i) q^{73} +(0.687042 - 0.0904507i) q^{74} +(3.42934 - 2.63142i) q^{75} +(1.59631 - 1.59631i) q^{76} +(-1.34979 - 0.281454i) q^{77} +(-5.39121 - 2.23311i) q^{78} +(2.22701 + 2.90230i) q^{79} +(0.652971 + 0.501042i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-4.43620 - 0.584036i) q^{82} +(3.72085 + 3.72085i) q^{83} +(1.19202 - 2.36201i) q^{84} +(-3.33900 - 0.605906i) q^{85} +(-1.62900 + 2.82151i) q^{86} +(0.0376653 - 0.140569i) q^{87} +(0.317254 - 0.413454i) q^{88} +(2.79672 + 1.61469i) q^{89} +(-0.760401 + 0.314968i) q^{90} +(-5.09731 + 14.5733i) q^{91} +(-3.70917 - 1.53639i) q^{92} +(1.24489 + 4.64601i) q^{93} +(5.07209 + 1.35906i) q^{94} +(0.242525 + 1.84216i) q^{95} +(0.608761 + 0.793353i) q^{96} +(-13.9878 + 5.79395i) q^{97} +(-6.41666 - 2.79759i) q^{98} +(0.199434 + 0.481477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} + 8 q^{10} + 16 q^{14} + 16 q^{15} + 48 q^{16} + 8 q^{17} + 48 q^{18} - 8 q^{19} + 16 q^{22} + 24 q^{25} + 32 q^{28} - 32 q^{29} - 16 q^{33} - 48 q^{37} - 16 q^{39} + 128 q^{41} + 16 q^{42}+ \cdots + 160 q^{97}+O(q^{100}) \) 96 * q + 8 * q^5 + 8 * q^10 + 16 * q^14 + 16 * q^15 + 48 * q^16 + 8 * q^17 + 48 * q^18 - 8 * q^19 + 16 * q^22 + 24 * q^25 + 32 * q^28 - 32 * q^29 - 16 * q^33 - 48 * q^37 - 16 * q^39 + 128 * q^41 + 16 * q^42 + 48 * q^43 - 8 * q^44 - 8 * q^46 - 112 * q^49 + 64 * q^50 - 16 * q^52 - 40 * q^53 + 16 * q^57 + 16 * q^58 - 24 * q^59 + 8 * q^60 - 56 * q^70 + 24 * q^73 + 48 * q^74 - 16 * q^76 + 16 * q^77 + 32 * q^78 - 56 * q^79 - 8 * q^80 - 80 * q^83 + 80 * q^85 + 16 * q^86 - 24 * q^87 + 16 * q^90 - 40 * q^91 + 16 * q^92 - 8 * q^93 - 8 * q^94 + 80 * q^95 + 160 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more